Inhomogeneous quantum quenches in the sine-Gordon theory

D. X. Horv\'ath; G. Tak\'acs; M. Kormos; S. Sotiriadis

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Inhomogeneous quantum quenches in the sine-Gordon theory

D. X. Horváth, M. Kormos, S. Sotiriadis, G. Takács

Strongly Correlated Electrons · Submitted 14 Sep 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial.

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arXiv ID2109.06869 (version 3)

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CitationD. X. Horv\'ath, G. Tak\'acs, M. Kormos, S. Sotiriadis. "Inhomogeneous quantum quenches in the sine-Gordon theory." arXiv:2109.06869 (2021). https://pith.science/paper/N54CMFVA

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.29 · mentions code or data availability 0.01.

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We study inhomogeneous quantum quenches in the attractive regime of the sine-Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine-Gordon Hamiltonian. Varying either the interaction strength of the sine-Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein-Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine-Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine-Gordon dynamics in arbitrary inhomogeneous settings.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study inhomogeneous quantum quenches in the attractive regime of the sine-Gordon model.	contribution 0.99	0.92	0.04	asserted 0.94
s1	In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field.	method 0.99	0.91	0.02	asserted 1.00
s2	After switching off the external field, the subsequent time evolution is governed by the homogeneous sine-Gordon Hamiltonian.	method 0.99	0.62	0.03	asserted 1.00
s3	Varying either the interaction strength of the sine-Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density.	result 1.00	0.92	0.25	asserted 0.99
s4	This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein-Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude.	result 0.72	0.89	0.33	asserted 0.95
s5	The transition in the initial state is also displayed by the classical sine-Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively.	interpretation 0.98	0.65	0.18	asserted 0.84
s6	Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution.	result 0.75	0.89	0.12	hedged possibility 0.84
s7	These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial.	interpretation 1.00	0.51	0.42	hedged possibility 0.99
s8	Nevertheless, their interplay is expected to influence the sine-Gordon dynamics in arbitrary inhomogeneous settings.	interpretation 0.90	0.13	0.23	hedged possibility 0.93

What kind of paper the classifier reports this is: simulation study 0.65 · evidence from simulation or computation 0.88.

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Original abstract

We study inhomogeneous quantum quenches in the attractive regime of the sine-Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine-Gordon Hamiltonian. Varying either the interaction strength of the sine-Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein-Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine-Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine-Gordon dynamics in arbitrary inhomogeneous settings.

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References

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Sine-Gordon Model with Bosonic Tensor Networks: Continuum Matching and Soliton Scattering
quant-ph 2026-09 accept novelty 8.0 of 10

Bosonic tensor networks reproduce the exact soliton mass, dispersion, and breather masses of the sine-Gordon model, and simulate soliton-antisoliton scattering with displacements matching continuum theory.
Universal Phase Locking from Slowly Varying Inhomogeneity in Tunnel-Coupled One-Dimensional Condensates
cond-mat.quant-gas 2026-11 conditional novelty 7.0 of 10

Phase locking in tunnel-coupled 1D condensates is caused by the local curvature of the density profile, with a timescale independent of tunnel coupling and captured by linearized modes.

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7 arXiv papers cite this in 14 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 9 sentences without a confident label

Uses its method or tool 1 paper

Here we briefly describe how to implement these optimisations in the framework of CFTCSA, first used in the work [ref] .

Chirally Factorised Truncated Conformal Space Approach · Computing matrix elements of creation/annihilation operators · 0.91

Compares with it 1 paper

In the following, demonstrate some results of Ref. [ref] focusing on the properties of the inhomogeneous ground state and also provide a benchmark for the validity of our results.

Chirally Factorised Truncated Conformal Space Approach · Inhomogeneous quenches in the sine-Gordon field theory · 0.90

Cites it as background 3 papers

Here we will focus on a class of inhomogeneous quenches that affect the system globally (for other studies on the topic see, , [ref] ). .

Boundary-induced transitions in M\"obius quenches of holographic BCFT · Entanglement entropy evolution under SSD and Möbius Hamiltonians · 1.00
They have also been used to study correlation functions [ref] , real time non-equilibrium dynamics [ref] , symmetry breaking [ref] , Kibble-Zurek mechanism [ref] , quantum chaos [ref] , confinement [ref] , spectral form factors [ref] and have been used to study genuinely field theoretical (continuum) phenomena [ref] .

Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation · Introduction · 0.86
The study of kinks in quenched theories has recently received attention in Ref. [ref] .

Spectral Walls at One Loop · Conclusion and Future Directions · 0.99

What it cites · 81 sentences without a confident label

Uses the method or tool of 2 papers

Our method of choice to investigate the dynamics is a variant of Hamiltonian truncation, the so-called truncated conformal space approach (TCSA) introduced in [ref] to describe the finite volume spectrum of perturbed minimal conformal field theories, and extended to the sine–Gordon model in [ref] .

Nonlinear Integral Equation and Finite Volume Spectrum of Sine-Gordon Theory · Introduction · 0.93
Our method of choice to investigate the dynamics is a variant of Hamiltonian truncation, the so-called truncated conformal space approach (TCSA) introduced in [ref] to describe the finite volume spectrum of perturbed minimal conformal field theories, and extended to the sine–Gordon model in [ref] .

Truncated Conformal Space at c=1, Nonlinear Integral Equation and Quantization Rules for Multi-Soliton States · Introduction · 0.93

Cites as background 26 papers

In particular, it has a fundamental role in the hydrodynamic description of one-dimensional integrable systems where integrability is violated by some spatial inhomogeneity [ref] .

Hydrodynamics of the interacting Bose gas in the Quantum Newton Cradle setup · Limitations of the local density approximation, and the transition in the free massive Dirac theory · 0.84
In particular, it has a fundamental role in the hydrodynamic description of one-dimensional integrable systems where integrability is violated by some spatial inhomogeneity [ref] .

Large-scale description of interacting one-dimensional Bose gases: generalized hydrodynamics supersedes conventional hydrodynamics · Limitations of the local density approximation, and the transition in the free massive Dirac theory · 0.84
In particular, it has a fundamental role in the hydrodynamic description of one-dimensional integrable systems where integrability is violated by some spatial inhomogeneity [ref] .

Quantum Generalized Hydrodynamics of the Tonks-Girardeau gas: density fluctuations and entanglement entropy · Limitations of the local density approximation, and the transition in the free massive Dirac theory · 0.84

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