Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods

Giovanni Cataldi

REVIEW 4 major objections 4 minor 2 cited by

Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A dressed-site formalism enables the first tensor-network simulations of two-dimensional SU(2) Yang-Mills lattice gauge theory, with an exact bosonic gauge-invariant encoding.

desk verdict A well-organized thesis compiling the author's own significant tensor-network results for SU(2) lattice gauge theories, but the headline phase diagram and scarring claims rest on a truncation whose validity is asserted, not demonstrated, and the rishon decomposition is left unproven. read the letter →

arxiv 2501.11115 v2 pith:N3KGUGTN submitted 2025-01-19 hep-lat cond-mat.str-elphysics.comp-phquant-ph

Giovanni Cataldi This is my paper · ORCID

classification hep-latcond-mat.str-elphysics.comp-phquant-ph

keywords latticegaugetheorytensornetworksdressed-siteformalismSU(2)Yang-Millsquantummany-bodyscarsfermion-to-qubitmappingHilbertcurveHamiltoniansimulation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This thesis claims that the dressed-site formalism, which fuses each lattice site with the neighboring truncated gauge-link degrees of freedom, gives an exact, bosonic, gauge-invariant reformulation of Hamiltonian lattice gauge theories with controllable truncation. Applied to SU(2) Yang-Mills with dynamical staggered fermions, it makes two-dimensional tensor-network simulations possible for the first time, producing a phase diagram at zero and finite baryon density plus a first observation of quantum many-body scarring in a non-Abelian lattice gauge theory. The broader claim is that tensor networks can access regimes, real-time dynamics and finite density, where Monte Carlo methods are blocked by the sign problem. If correct, the formalism provides a practical route from Abelian toy models toward non-Abelian theories relevant for QCD, and a benchmark target for quantum simulators.

What carries the argument

The central object is the dressed site: a composite degree of freedom formed by fusing a staggered-fermion matter site with the rishon modes of all attached half-links. Each truncated gauge link is split into two rishons; the parallel transporter becomes a rishon bilinear, and the requirement that the two sides of a link sit in the same irreducible representation becomes an Abelian $\mathbb Z_2$ link symmetry. Gauss law is then a purely internal constraint, and the effective Hamiltonian is obtained by projecting onto its kernel, yielding local, bosonic operators.

What would settle it

Repeat the reported two-dimensional ground-state phase diagram and the one-dimensional scar-revival calculations with link truncations $j_{\max}=1$, $3/2$, and higher on the same lattice sizes; if the phase-boundary locations and the revival fidelity of the scarred states change substantially or disappear as $j_{\max}$ is increased, the claimed signatures are artifacts of the truncation rather than properties of full SU(2) Yang-Mills.

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Extended reading notes

Core claim

Within the hardcore-gluon truncation ($j_{\max}=1/2$) of SU(2) Yang-Mills, the parallel transporter on each link is decomposed into two fermionic rishon modes, one per half-link; the rishons are then absorbed into the adjacent matter site, and Gauss' law is imposed exactly by restricting to the kernel of the gauge generators. The resulting dressed-site Hamiltonian is made entirely of bosonic operators acting on a 30-dimensional local basis in two spatial dimensions, so fermionic statistics and gauge constraints no longer need to be enforced dynamically. Using this representation, the thesis reports the first tensor-network ground-state and time-evolution simulations of two-dimensional SU(2) Yang-Mills lattice gauge theory, including a magneto-electric crossover, baryonic spectrum, a finite-density baryon-liquid phase, and topological sectors, together with quantum many-body scarring dynamics in the one-dimensional truncation.

Load-bearing premise

The load-bearing premise is that the minimal hardcore-gluon truncation, keeping only the $j=0$ and $j=1/2$ representations of the SU(2) link field, faithfully captures the low-energy physics in the regimes where the phase diagram and scarring dynamics are computed, although the thesis states this truncation is reliable mainly for strong coupling $g\gg1$.

Editorial extensions

If this is right

Gauss law is satisfied by construction, so no large penalty terms are needed to keep the simulation in the physical gauge-invariant sector.
Because every term in the effective Hamiltonian is bosonic, tensor-network algorithms avoid both the Monte Carlo sign problem and long-range fermion-to-qubit encodings.
The compact local dimensions, 30 per site in the two-dimensional hardcore-gluon case, make exact diagonalization and moderate-bond tensor networks feasible, while the dressed-site dimension grows rapidly with truncation level.
The reported finite-density phase diagram and non-equilibrium scar dynamics are concrete observables that can serve as benchmarks for future quantum simulations of non-Abelian gauge theories.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the exactness of the dressed-site mapping holds at every truncation level, the same construction should extend to SU(3) Yang-Mills; the practical obstacle would be the much larger local Hilbert space rather than gauge invariance.
The thesis reports scar signatures at higher link truncations but not extrapolated to the continuum; a direct test is whether revivals and the scar tower survive as $j_{\max}$ grows toward the weak-coupling limit.
The fermion-to-qubit mapping developed for general lattice fermion theories could be applied to other fermionic condensed-matter models, where it may reduce the qubit overhead of digital quantum simulation beyond the Hubbard example studied here.
The Hilbert-curve ordering result and the dressed-site formalism are developed in parallel; combining them systematically in two-dimensional lattice gauge theory simulations is a natural next step that the thesis does not itself carry out.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Giovanni, quick take on arXiv:2501.11115. It's a PhD thesis that compiles the author's own published work, mostly already in peer-reviewed venues (PRR, Quantum). What is actually new here is the exposition: a self-contained derivation of the dressed-site formalism for SU(2) and U(1), with explicit bases for the hardcore-gluon model, plus a chapter on fermion-to-qubit mapping and realistic discussion of Hilbert curve ordering for 2D tensor networks. The thesis is honest about being a compilation, and it ships code (ed-lgt, Zenodo DOI) that reproduces the dressed-site operators. That is real.

The central physics claims are the first tensor-network simulations of 2D SU(2) Yang-Mills at finite density and quantum many-body scarring in a 1D truncated SU(2) model. If those results are right, they are significant: they extend TN methods to non-Abelian gauge theories beyond 1D, in regimes Monte Carlo can't reach. The simulations themselves are numerical and not independently reproducible from the arXiv artifact, but the published papers and the released code go a long way.

The soft spots are two. The rishon decomposition of the SU(2) parallel transporter is asserted with 'it is possible to show' (Sec. 1.3.3, around Eqs. 1.3.23-1.3.31), and the projected dressed-site Hamiltonian (Eq. 1.3.45) lacks a full derivation. That's a tractable gap: either prove it in an appendix or cite where the supplementary derivation is available. It didn't stop me from following the construction, but a referee should insist.

The more serious issue is the use of the jmax=1/2 hardcore-gluon truncation for the phase diagram and scar claims. In Sec. 1.3.5 the thesis itself limits this truncation to g >> 1, where the electric term dominates. The magneto-electric transition in Chapter 3 happens near where the magnetic term becomes important, i.e. not clearly in the strong-coupling regime, and the scarring in Chapter 4 is in the same truncated model. No convergence check in jmax is provided for these observables. The U(1) truncation analysis in Sec. 1.4.5 shows similar truncations converge poorly at small g, so the risk is real: the reported boundaries and scar revivals may be properties of the hardcore-gluon model, not of SU(2) Yang-Mills. The exactness of the dressed-site mapping for a fixed truncation does not address this, and the stress-test note is right on this point.

Who is this for? People entering Hamiltonian LGT simulations, tensor network experts looking for a gauged reference, and quantum simulation groups benchmarking qudit encodings. It does a good pedagogical job.

My recommendation: yes, send it to peer review, but with a referee pitch that requires (1) a complete proof of the rishon decomposition, and (2) truncation-error quantification for the phase diagram, e.g. jmax=1 comparisons or strong-coupling perturbation theory. If those are added, the thesis becomes a useful reference. As is, it's a promising but incomplete presentation of important results.

Referee Report

4 major / 4 minor

Summary. This manuscript, a PhD thesis posted on arXiv, develops a dressed-site formalism for Hamiltonian lattice gauge theories in which gauge links are truncated by an energy cutoff, decomposed into fermionic rishon modes, and fused with matter sites into gauge-invariant dressed sites with bosonic statistics. The formalism is applied to SU(2) Yang-Mills with staggered matter in two spatial dimensions, where the author reports ground-state phase diagrams, baryonic spectra, a baryon-liquid phase, topological observables, and, in a one-dimensional truncated model, quantum many-body scarring dynamics. The thesis also presents a fermion-to-qubit mapping for general lattice fermion theories, an analysis of space-filling curves for tensor-network locality, and a roadmap for high-performance tensor-network simulations of lattice gauge theories.

Significance. If the central formal claim is correct, the dressed-site construction provides an exact, gauge-invariant, bosonic encoding of truncated non-Abelian gauge theories, and the reported (2+1)D SU(2) simulations would be a genuinely new tensor-network application. The manuscript is also useful as a systematic review of tensor-network methods for lattice gauge theories, and the accompanying ED-LGT code and the quantum-simulation oriented qudit formulation are concrete contributions that go beyond a purely pedagogical treatment. However, the significance of the headline physical results—phase diagram and many-body scarring—depends on two points that are not adequately established in the manuscript: the exactness of the rishon decomposition of the parallel transporter for arbitrary truncation, and the quantitative validity of the hardcore-gluon jmax=1/2 truncation in the regime where the reported transitions and dynamics occur. The paper should be credited for including numerical evidence of truncation convergence for a single QED plaquette, but that evidence is not carried over to the SU(2) calculations.

major comments (4)

[Sec. 1.3.3, Eqs. (1.3.23)–(1.3.31)] The central formal step—the rishon decomposition of the truncated SU(2) parallel transporter—is asserted rather than proved. After Eq. (1.3.27) the text says “It is possible to show that this construction is indeed compatible with the explicit form of the parallel transport reported in Eq. (1.3.10),” but no proof or explicit algebraic verification is given. Since all subsequent dressed-site operators and all numerical results in Chapters 3 and 4 inherit this equivalence, this is load-bearing. The author should either provide a complete derivation, or a reproducible symbolic/numerical verification that the right-hand side of Eq. (1.3.23) equals the Clebsch-Gordan matrix elements of Eq. (1.3.10) for all allowed j and for generic jmax.
[Sec. 1.3.4, Eq. (1.3.45)] The ‘operative defermionized Hamiltonian’ is written down without a complete step-by-step derivation. In particular, the passage from the rishon form of the hopping and plaquette terms to the projected dressed-site operators uses the projection Oeff = M†OM of Eq. (1.2.5), but the text does not show how the 5×5 or 30×30 dressed-site matrices are obtained, what the explicit coefficients of the corner operators are, or how the Gauss-law kernel M is computed in practice. This is not merely a presentation issue, because the correctness of Eq. (1.3.45) is the basis for every reported numerical result. The author should add a derivation or an appendix with the operator construction, and should state explicitly which results are independently reproducible from the released ed-lgt code.
[Sec. 1.3.5 and Ch. 3, esp. Sec. 3.2 and 3.7] The hardcore-gluon truncation jmax=1/2 is described in Sec. 1.3.5 as a good approximation only in the strong-coupling limit g >> 1, and Sec. 1.3.2 states that weak-coupling continuum physics requires larger representations. Yet Chapter 3 reports a magneto-electric transition and a phase diagram for (2+1)D SU(2) Yang-Mills. The magneto-electric crossover occurs where the magnetic plaquette term, suppressed by 1/g^2, balances the electric term; by the author’s own criterion this is precisely the regime where jmax=1/2 is least justified. No convergence check in jmax is reported for the 2D equilibrium results, and the single-plaquette convergence study of Fig. 1.3 is performed for U(1), not SU(2). The author should either (i) identify the coupling range of the reported transition and demonstrate that jmax=1/2 is reliable there, or (ii) explicitly rephrase the Chapter 3 results as properties of the truncated hardcore-gluon model rather than of SU(2) Yang-Mills.
[Sec. 1.4.5, Fig. 1.3] The text uses the QED plaquette convergence result ℓ* ~ g^-1 to motivate the statement that “an analogous inverse dependence of the minimal gauge truncation on the coupling is expected for non-Abelian LGT in arbitrary dimensions.” This expectation is not demonstrated, and it is invoked in discussing the need for truncation compression. The author should either supply a corresponding single-plaquette or small-lattice convergence study for SU(2), or clearly label this statement as an unsupported conjecture. Since the abstract claims the first TN simulations of the 2D SU(2) system, this missing truncation benchmark is directly relevant to whether the reported physics is the physics of the full gauge theory.

minor comments (4)

[Throughout] The manuscript contains numerous typographical and notational infelicities, including “Cliffor’s algebra” (Sec. 1.1.4), the anticommutator sign in Eq. (1.3.4), duplicated figure labels (Fig. 1.1 and Fig. 1.2), and inconsistent placement of subscripts such as ψˆ†n,α vs ψˆ†n,α. A careful proofreading pass would substantially improve readability.
[Sec. 1.3.3, Eq. (1.3.27)] The definition of the rishon operator ζˆg(r) is hard to parse: the lower limit of the sum is written as “jmax− 1/2” and the index m− in the ket ⟨j+1/2, m−+1/2| is not defined. This should be restated with explicit bounds and a clear explanation of the truncated Hilbert space to allow the reader to verify Eq. (1.3.27).
[Sec. 3.1 and Abstract] The abstract’s claim of “first TN simulations” relies on the author’s own publication [2]. A short review of prior tensor-network or other Hamiltonian approaches to (1+1)D and (2+1)D non-Abelian gauge theories would help place this claim in context and distinguish a first in a specific truncation scheme from a first for the full model.
[Sec. 1.3.5, Eqs. (1.3.57a)–(1.3.57d)] In the 1D qudit Hamiltonian Eq. (1.3.59), the operator Mˆ n appears in the mass term but was not explicitly defined in the preceding equations; Eq. (1.3.57c) defines Nˆ n, and the text later uses Mˆ n. The author should define Mˆ n explicitly or replace it by Nˆ n for consistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dressed-site derivation and the numerical simulations are self-contained, while the hardcore-gluon truncation is an explicit validity limitation rather than a circular input.

full rationale

The thesis's derivation chain is not circular at the equation level. The lattice Hamiltonian is obtained from the standard Kogut-Susskind construction, the gauge-field truncation is defined by a Casimir cutoff, the rishon decomposition is introduced as an algebraic rewriting, and the dressed-site operators are obtained by projecting onto the kernel of the Gauss-law constraint. The reported phase diagram and scar dynamics are outputs of explicit diagonalizations and tensor-network simulations of that well-defined truncated Hamiltonian, not fits designed to reproduce the claimed conclusions. The hardcore-gluon approximation jmax=1/2 is explicitly stated in Sec. 1.3.5 to be reliable only in the strong-coupling limit g≫1, and Sec. 1.3.2 says that weak-coupling physics requires larger representations; the absence of a jmax-convergence check is a legitimate correctness risk for extrapolating to the full SU(2) theory, but it is not circularity. The self-citations to the author's own papers [2-5] support the priority claim and the roadmap framing, but the underlying numerical results are independent outputs of the stated model, and no fitted parameter is renamed as a prediction. The 'first TN simulations' claim is a bibliographic assertion supported by a self-citation rather than a derivation, so it does not make the physical derivation circular. Overall, the central derivation reduces to standard Hamiltonian lattice gauge theory plus an explicit truncation, not to its own conclusions.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new physical particles, forces, or dimensions are posited. The rishon modes and dressed sites are auxiliary mathematical bookkeeping devices used to reorganize the gauge degrees of freedom; they carry no independent falsifiable predictions. The free parameters are the gauge truncation choices that control the local Hilbert space dimension.

free parameters (2)

Hardcore-gluon truncation jmax = 1/2
The smallest non-trivial SU(2) truncation, imposed by hand in Sec. 1.3.5 to make tensor network simulations tractable. The thesis acknowledges it is reliable only for strong coupling, yet the phase diagram in Ch3 uses it.
Gauge truncation cutoff Theta = jmax(jmax+1)
Energy cutoff on the Casimir spectrum introduced in Sec. 1.2.1. This controls the local dressed-site Hilbert space dimension and is a free numerical parameter of the formalism.

assumptions (4)

domain assumption Truncating the gauge group by a Casimir energy cutoff preserves the relevant low-energy physics of the untruncated theory.
Invoked in Secs. 1.2.1 and 1.3.5. The paper states this is justified in the strong-coupling limit, but the truncation error is not quantified and the continuum limit requires larger jmax (Sec. 1.4.5).
ad hoc to paper The rishon decomposition U = zeta zeta^dagger with zeta defined in Eq. (1.3.27) exactly reproduces the SU(2) parallel transporter for all jmax.
Sec. 1.3.3, Eq. (1.3.23)-(1.3.27). The paper says 'It is possible to show' the compatibility with Eq. (1.3.10), but no proof is provided. This construction is the core of the dressed-site Hamiltonian.
domain assumption Staggered fermions with the phase factors in Eq. (1.1.32) give a valid lattice discretization of Dirac fermions.
Standard Kogut-Susskind staggered fermion assumption, adopted from [144,148]. The thesis relies on it without re-deriving or justifying the continuum limit.
domain assumption The Z2 link symmetry constraint, equality of the two rishon Casimirs, is exactly equivalent to the original SU(2) link gauge invariance.
Sec. 1.3.4, Eq. (1.3.36). This reduction of non-Abelian link symmetry to an Abelian Z2 selection rule is central to the dressed-site approach, but its exactness for the truncated gauge group is asserted rather than proven.

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Cite this review

Pith. "Pith review of Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods." pith.science (2026). https://pith.science/paper/N3KGUGTN

@misc{pith2026250111115,
  author       = {Pith},
  title        = {Pith review of: Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N3KGUGTN}},
  note         = {Machine review of arXiv:2501.11115}
}

read the original abstract

This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields while preserving gauge invariance for both Abelian and non-Abelian theories. This formalism is successfully applied to SU(2) Yang-Mills LGTs in two dimensions, providing the first TN simulations of this system and revealing critical aspects of its phase diagram and non-equilibrium behavior, such as a Quantum Many-Body (QMB) scarring dynamics. A generalization of the dressed-site formalism is proposed through a new fermion-to-qubit mapping for general lattice fermion theories, revealing powerful for classical and quantum simulations. Numerical innovations, including the use of optimal space-filling curves such as the Hilbert curve to preserve locality in high-dimensional simulations, further enhance the efficiency of these methods. Together with high-performance computing techniques, these advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art.

Figures

Figures reproduced from arXiv: 2501.11115 by the authors.

**Figure 1.3.** Exact diagonalization of a QED plaquette for a grid of masses [PITH_FULL_IMAGE:figures/full_fig_p047_1_3.png] view at source ↗

**Figure 2.1.** Illustration of block diagonalization. In absence of symmetries, we have to diagonalize [PITH_FULL_IMAGE:figures/full_fig_p051_2_1.png] view at source ↗

**Figure 2.2.** Pictorial representation of the main manipulations (a)-(c), contractions (d), and [PITH_FULL_IMAGE:figures/full_fig_p056_2_2.png] view at source ↗

Figures from the paper (32 more)

**Figure 2.4.** Figure 2.4: Pictorial representation of the employment of unitary gauges on a TN structure [PITH_FULL_IMAGE:figures/full_fig_p062_2_4.png]

**Figure 2.5.** Figure 2.5: Iterative construction of the space-filling Hilbert curve on an [PITH_FULL_IMAGE:figures/full_fig_p067_2_5.png]

**Figure 2.6.** Figure 2.6: Numerical simulations of the 2D quantum Ising Hamiltonian at [PITH_FULL_IMAGE:figures/full_fig_p068_2_6.png]

**Figure 2.7.** Figure 2.7: Local magnetization difference between the Hilbert and the snake ground states for [PITH_FULL_IMAGE:figures/full_fig_p069_2_7.png]

**Figure 2.8.** Figure 2.8: Distributions of the number of TN links separating physically adjacent lattice sites in [PITH_FULL_IMAGE:figures/full_fig_p069_2_8.png]

**Figure 2.9.** Figure 2.9: Distributions of the distances dMPS (first row) and dTTN (second row) relative to the pairs of sites connected by an interaction term in the Hamiltonian Hˆ H computed for n = 16 (first column) and n = 32 (second column). MPS and the Hilbert curve is larger than the o…

**Figure 2.10.** Figure 2.10: (a) Pictorial representation of the variational ground-state search algorithm w.r.t a [PITH_FULL_IMAGE:figures/full_fig_p075_2_10.png]

**Figure 2.11.** Figure 2.11: Graphical representation of (a) the pseudo site DMRG (PS-DMRG) approach, [PITH_FULL_IMAGE:figures/full_fig_p078_2_11.png]

**Figure 2.12.** Figure 2.12: Effective operators and parallel tensor networks. (a) Procedure for optimizing a TTN to find the ground state of a QMB system: the energy is computed by contracting the Hamiltonian Hˆ (yellow tensor) with the TTN, representing the state |ψ⟩, and its hermitian conjug…

**Figure 3.1.** Figure 3.1: TTN approach to (2+1)D SU(2) Yang-Mills LGT. Lattice sites host flavorless SU(2)- [PITH_FULL_IMAGE:figures/full_fig_p088_3_1.png]

**Figure 3.2.** Figure 3.2: Numerical simulations of the pure Hamiltonian in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p090_3_2.png]

**Figure 3.3.** Figure 3.3: (a) Scaling of the particle density defined in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p092_3_3.png]

**Figure 3.4.** Figure 3.4: Numerical results of the full SU(2) Hamiltonian in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p094_3_4.png]

**Figure 3.5.** Figure 3.5: Simulations of the full SU(2) Hamiltonian in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p095_3_5.png]

**Figure 3.6.** Figure 3.6: Simulations of a 2 × 2 lattice in PBC. The plots display respectively: (a) the average particle density ϱ and (b) its quantum fluctuations δϱ; (c) the matter color density ⟨S 2 matt⟩ and (d) its quantum fluctuations δS2 matt. All the observables are studied as a func…

**Figure 3.7.** Figure 3.7: Pictorial representations of the topological invariants defined in Eqs. ( [PITH_FULL_IMAGE:figures/full_fig_p098_3_7.png]

**Figure 3.8.** Figure 3.8: Distance between the ground-state Py-topological invariant in the full theory and the corresponding one of the pure theory for different m-values (a) and g-couplings (b). Results from simulations in a 2 × 2 lattice with PBC at b = 0. Figure from [2]. the case of an-i…

**Figure 3.9.** Figure 3.9: Graphical representation of the 1 st and 2 nd order perturbative effects of the magnetic (a) and the hopping terms (b)-(c) to the ground state of Eq. (3.6.2). while the perturbative terms read: Hˆ matt n = m(−1)nx+nyNˆ n,tot (3.6.3a) Hˆ x-hop n = 1 2 [︂ −iQˆ † n,+µx …

**Figure 3.10.** Figure 3.10: Phase diagram (g 2 , m) of the full SU(2) Hamiltonian in Eq. (3.1.2) in the sector with zero baryon number density from (a) the average electric energy density in Eq. (3.1.4), (b) the average particle density in Eq. (3.1.7), and (c) the matter color density defined …

**Figure 4.1.** Figure 4.1: Many-body scarring dynamics of the polarized bare vacuum (left) and the bare [PITH_FULL_IMAGE:figures/full_fig_p116_4_1.png]

**Figure 4.2.** Figure 4.2: Spectrum analysis for a lattice chain of [PITH_FULL_IMAGE:figures/full_fig_p118_4_2.png]

**Figure 4.3.** Figure 4.3: Dynamics of the microcanonical state in Eq. (4.4.10) for the same parameter regimes of [PITH_FULL_IMAGE:figures/full_fig_p119_4_3.png]

**Figure 4.4.** Figure 4.4: [Left]: Many-body spectrum. Spectrum analysis for a lattice chain of N = 10 sites with open boundary conditions in a few paradigmatic regimes (corresponding to different columns) where we observe ergodic dynamics. The first and second rows show the overlap of the man…

**Figure 4.5.** Figure 4.5: Scarring at higher gauge truncation. Many body scarring dynamics for the polarized bare vacuum (PV) and the bare vacuum (V) for the truncated SU(2) YM LGT at jmax = 1 (pink line) in comparison with the corresponding one at jmax = 1/2 (cyan line). Each column reports …

**Figure 4.6.** Figure 4.6: Finite-size scaling. Return fidelity during the evolution of the polarized bare vacuum (a) and bare vacuum (b) initial states, for m = 5, g 2 = 1, open boundary conditions, and various systems sizes N. The side plots (c) and (d) show the finite-size scaling of the hi…

**Figure 4.7.** Figure 4.7: Long time dynamics. First to third row: return fidelity, average quark occupancy, and bipartite entanglement entropy as a function of time for the two initial states: polarized bare vacuum, and bare vacuum. We considered different values of mass and coupling as indic…

**Figure 5.1.** Figure 5.1: Simulation of the Hubbard model in 2D with tensor networks (equilibrium) and [PITH_FULL_IMAGE:figures/full_fig_p126_5_1.png]

**Figure 5.2.** Figure 5.2: Exact Diagonalization comparison on a 2×2 lattice between the ground state energy density ε of the original 2D Hubbard model and its defermionized version as a function of U/t, and for three values of the particle density ρ: (a) below half-filling with ρ = 0.5, (b) a…

**Figure 5.3.** Figure 5.3: (a) Ground state energy density of the 2D Hubbard Hamiltonian at [PITH_FULL_IMAGE:figures/full_fig_p134_5_3.png]

**Figure 5.5.** Figure 5.5: Mapping of the time propagator of a generic Pauli string to a quantum circuit using [PITH_FULL_IMAGE:figures/full_fig_p139_5_5.png]

**Figure 5.6.** Figure 5.6: Graphical representation of the Hamiltonian terms in the defermionized Hubbard [PITH_FULL_IMAGE:figures/full_fig_p141_5_6.png]

**Figure 5.7.** Figure 5.7: Schematic of injecting spin- and charge-excitations on the [PITH_FULL_IMAGE:figures/full_fig_p142_5_7.png]

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Forward citations

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Neural quantum states for non-Abelian lattice gauge theories with dynamical fermions
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A sign-problem-free variational Monte Carlo framework computes ground states of continuous SU(2) lattice gauge theory with dynamical fermions, matching strong-coupling perturbation theory and sketching the (g², λ) pha...
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An untruncated variational Monte Carlo study finds a magnetic-flux transition at λ*≈−0.040 and a weak-to-strong coupling delocalization crossover in 2+1D SU(2) lattice gauge theory with staggered fermions.

Reference graph

Works this paper leans on

299 extracted references · 116 canonical work pages · cited by 2 Pith papers

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Hilbert Curve vs Hilbert Space: Exploiting Fractal 2D Covering to Increase Tensor Network Efficiency

Giovanni Cataldi, Ashkan Abedi, Giuseppe Magnifico, Simone Notarnicola, Nicola Dalla Pozza, Vittorio Giovannetti, and Simone Montangero. “Hilbert Curve vs Hilbert Space: Exploiting Fractal 2D Covering to Increase Tensor Network Efficiency”.Quantum, Sept. 2021.doi: 10.22331/q-2021-09-29-556

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Quantum Many-Body Scarring in a Non-Abelian Lattice Gauge Theory

Giovanni Cataldi*, Giuseppe Calajó*, Marco Rigobello, Darvin Wanisch, Giuseppe Magnifico, Pietro Silvi, Simone Montangero, and Jad C. Halimeh. “Quantum Many-Body Scarring in a Non-Abelian Lattice Gauge Theory”.Physical Review Research, Mar. 2025.doi: 10.1103/PhysRevResearch.7.013322

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