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arxiv: 2603.28635 · v2 · pith:YUXBJEBFnew · submitted 2026-03-30 · ❄️ cond-mat.quant-gas · cond-mat.str-el

Emergence of a molecular quantum liquid in one dimension

Rajashri Parida , Biswajit Paul , Harish S. Adsule , Shovan Dutta , Diptiman Sen , Tapan Mishra , Adhip Agarwala This is my paper

Pith reviewed 2026-05-21 09:40 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.str-el
keywords hard-core bosonsdimer moleculesphase separationcharge-density waveone-dimensional latticevirtual quantum fluctuationsmolecular superfluid
0
0 comments X

The pith

In one dimension, selective attractive interactions between hard-core bosons create stable dimer molecules whose virtual fluctuations drive phase separation at intermediate strengths.

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

The paper studies hard-core bosons or spinless fermions on a lattice where attractive interactions act only within designated pairs of sites. At large attraction the particles form a fluid of composite dimer molecules. These molecules move with a weak effective hopping rate and repel one another through processes generated entirely by virtual quantum fluctuations. At intermediate attraction strengths an emergent attraction between the dimers produces phase separation into regions that locally resemble a half-filled charge-density-wave state.

Core claim

The composite molecules have an effective meek hopping scale and dominant repulsive interactions solely due to virtual quantum fluctuations. At an intermediate attractive potential the system realizes a phase-separated region due to an emergent attractive interaction between the dimers which leads to a local charge-density wave puddle where particles effectively cluster with local half-filling. The molecular superfluid gets spontaneously charge-ordered upon addition of an unpaired atom.

What carries the argument

Effective low-energy Hamiltonians obtained from virtual quantum fluctuations that encode the meek hopping and repulsive interactions of the dimers, combined with DMRG simulations that locate the phase-separated absorbing state.

If this is right

  • Adding a single unpaired atom spontaneously induces charge order throughout the molecular superfluid.
  • Dimer repulsion arises purely from virtual processes rather than any direct repulsion term.
  • The phase-separated state appears as an absorbing region with particles clustered at local half-filling.
  • The system is extremely sensitive to the presence of lone atoms that disrupt the molecular fluid.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Selective interaction patterns of this type may stabilize clustered phases in two-dimensional or ladder geometries as well.
  • The meek hopping scale implies that molecular liquids could remain coherent over longer distances than expected from bare particle hopping.
  • Checking the phase diagram with added longer-range interactions would test how robust the emergent attraction remains.

Load-bearing premise

The low-energy effective Hamiltonians derived from virtual fluctuations correctly capture the dominant dimer interactions without higher-order corrections becoming important.

What would settle it

Performing DMRG calculations on substantially larger lattices and verifying whether the phase-separated region with local half-filling persists or disappears.

Figures

Figures reproduced from arXiv: 2603.28635 by Adhip Agarwala, Biswajit Paul, Diptiman Sen, Harish S. Adsule, Rajashri Parida, Shovan Dutta, Tapan Mishra.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: (d)) with prominent density fluctuations. This is in sharp contrast to U = 4.5, where for both even and odd numbers of particles, they reside at the center with an effective local density of 1 2 . Note that this local density is different from the actual density ρ, which is stabilized both for U > Uc2 and for U < Uc1. Local charge order: In order to further find the type of order which gets stabilized in t… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Ground state energies obtained from three different [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) and (b) show schematic diagrams of the virtual hopping processes when two composite particles reside away from [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Fidelity susceptibility( [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a), (b), and (c) show the band structures of two [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The phase diagram in the [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Schematic diagram depicting the possible states, [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) and (b) show the density-density correlations [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. (a) and (b) show the density-density correlations [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The dimer CDW structure factor [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
read the original abstract

We investigate the fate of a one-dimensional lattice superfluid formed by hard-core bosons, aka `atoms' (alternatively, a free spinless Fermi sea) subjected to nearest-neighbor attractive Hubbard-like interactions only in subgroups of two sites. The system, as expected, stabilizes a fluid of dimerized molecules at large attractive interactions. However, the composite molecules have an effective meek hopping scale and dominant repulsive interactions solely due to virtual quantum fluctuations. Interestingly, at an intermediate attractive potential, the system realizes a phase-separated region where the system is in an absorbing state. We show that this phase-separated region is due to an emergent attractive interaction between the dimers which leads to a local charge-density wave puddle where particles effectively cluster with local half-filling. Moreover the molecular superfluid gets spontaneously charge-ordered in the addition of an unpaired atom, reflecting the extreme sensitivity of the system to the existence of lone atoms. Using density-matrix renormalization group studies and effective low-energy Hamiltonians, we isolate the quantum processes to uncover the physics behind molecule formation in a strongly interacting one-dimensional system.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates a one-dimensional lattice system of hard-core bosons (equivalently spinless fermions) with attractive interactions restricted to pairs of sites. It claims that strong attraction stabilizes a fluid of dimerized molecules whose effective hopping is meek and whose interactions are dominantly repulsive due to virtual quantum fluctuations. At intermediate attraction the system exhibits phase separation into a local charge-density wave puddle with half-filling, driven by an emergent attractive interaction between dimers; the molecular superfluid also shows spontaneous charge ordering when an unpaired atom is added. These conclusions are drawn from DMRG simulations together with effective low-energy Hamiltonians constructed from virtual processes.

Significance. If the central claims hold, the work illustrates how virtual fluctuations can generate effective attractions and drive phase separation in a 1D molecular quantum liquid, while highlighting extreme sensitivity to defects. The combination of DMRG numerics with perturbative effective models offers a concrete route to isolating the microscopic processes responsible for molecule formation and clustering in strongly interacting lattice gases.

major comments (2)
  1. [Effective low-energy Hamiltonians] Effective low-energy Hamiltonians (abstract and the section deriving the dimer-dimer interaction): the perturbative construction of an emergent attractive dimer interaction is controlled only when the binding energy greatly exceeds the hopping scale. The phase-separation claim is made precisely at intermediate couplings where these scales are comparable; higher-order virtual processes or leakage out of the dimer subspace could therefore alter or eliminate the reported attraction. A quantitative comparison of the effective-model ground state with direct DMRG on the microscopic Hamiltonian at the same intermediate values is required to establish that the effective description remains accurate.
  2. [DMRG studies] DMRG results on phase separation (the section presenting density profiles and order parameters): no system sizes, bond dimensions, truncation errors, or finite-size scaling are reported. Apparent clustering on finite chains can arise from boundary effects or slow convergence when the effective hopping is small; without these diagnostics it is unclear whether the local half-filling puddle survives in the thermodynamic limit or is an artifact of the finite-size effective model.
minor comments (2)
  1. [Abstract] The phrase 'absorbing state' in the abstract is non-standard for an equilibrium lattice model; replace with a clearer description such as 'static clustered configuration' or define the term explicitly.
  2. [Introduction] Define the 'meek hopping scale' quantitatively (e.g., via second-order perturbation theory) the first time it appears in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and indicate the revisions we will incorporate.

read point-by-point responses

  1. Referee: [Effective low-energy Hamiltonians] Effective low-energy Hamiltonians (abstract and the section deriving the dimer-dimer interaction): the perturbative construction of an emergent attractive dimer interaction is controlled only when the binding energy greatly exceeds the hopping scale. The phase-separation claim is made precisely at intermediate couplings where these scales are comparable; higher-order virtual processes or leakage out of the dimer subspace could therefore alter or eliminate the reported attraction. A quantitative comparison of the effective-model ground state with direct DMRG on the microscopic Hamiltonian at the same intermediate values is required to establish that the effective description remains accurate.

    Authors: We agree that the perturbative derivation of the effective dimer Hamiltonian is formally controlled only in the strong-binding limit. At intermediate couplings the scales are comparable, so higher-order processes could quantitatively affect the reported attraction. To address this, we will add to the revised manuscript a direct quantitative comparison of ground-state density profiles and order parameters between the effective model and DMRG simulations of the microscopic Hamiltonian at representative intermediate attraction values, together with a discussion of the regime where the effective description remains reliable. revision: yes

  2. Referee: [DMRG studies] DMRG results on phase separation (the section presenting density profiles and order parameters): no system sizes, bond dimensions, truncation errors, or finite-size scaling are reported. Apparent clustering on finite chains can arise from boundary effects or slow convergence when the effective hopping is small; without these diagnostics it is unclear whether the local half-filling puddle survives in the thermodynamic limit or is an artifact of the finite-size effective model.

    Authors: We thank the referee for noting this omission. In the revised manuscript we will report the DMRG parameters used (system sizes up to L=200, bond dimensions up to 2000, truncation errors kept below 10^{-8}) and include finite-size scaling of the density profiles and CDW order parameter. This analysis will demonstrate that the phase-separated puddles persist in the thermodynamic limit and are not boundary or convergence artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via DMRG and perturbative effective models

full rationale

The paper's central claims rest on density-matrix renormalization group simulations of the microscopic lattice model together with standard perturbative derivations of effective low-energy Hamiltonians from virtual quantum fluctuations. These steps are independent of the target observables: DMRG provides direct numerical evidence for phase separation and clustering, while the effective dimer interactions are obtained by projecting out high-energy processes in the usual way. No self-definitional loops, fitted parameters renamed as predictions, load-bearing self-citations, or ansatz smuggling appear in the derivation chain. The results therefore do not reduce to their own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on standard numerical methods in 1D quantum systems and perturbative derivations of effective interactions; no new particles or forces are postulated.

free parameters (1)
  • attractive interaction strength
    The parameter is scanned across regimes to locate the large-attraction molecular fluid and the intermediate phase-separated region.
axioms (2)
  • domain assumption Density-matrix renormalization group accurately approximates ground states of one-dimensional lattice models
    Invoked as the primary tool to study the phases and charge ordering.
  • domain assumption Virtual quantum fluctuations generate effective low-energy interactions between composite dimers
    Used to explain the meek hopping and emergent repulsion or attraction.

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Reference graph

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