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arxiv: 2604.14367 · v1 · submitted 2026-04-15 · ❄️ cond-mat.str-el · cond-mat.other

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A Generalized Coherent State Framework for Many-Body Density of States

Deniz Coskun , R. Chitra
Authors on Pith no claims yet

Pith reviewed 2026-05-10 11:47 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.other
keywords many-body density of statesgeneralized coherent statesSimon-Lieb boundsquantum phase transitionsexcited-state quantum phase transitionsirreducible sectorsmicrocanonical observablesinteracting quantum systems
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The pith

Generalized coherent states combined with partition function bounds calculate the many-body density of states in high-dimensional symmetry sectors.

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

The paper develops a framework for computing the density of states in isolated interacting quantum systems by combining the generalized coherent state formalism with Simon-Lieb bounds on the quantum partition function. This approach targets high-dimensional irreducible sectors where direct calculations are difficult and supplies rigorous bounds on ground-state energies within each sector. It also permits extraction of microcanonical observables across the full spectrum. Validation on the Lipkin-Meshkov-Glick model recovers both quantum phase transitions and excited-state quantum phase transitions, while application to a power-law Ising chain shows that its highest-spin sector density of states matches the LMG case. The method rests on underlying symmetries rather than model-specific details, offering a route to many-body thermodynamics that remains computationally efficient.

Core claim

The authors establish that the generalized coherent state formalism together with Simon-Lieb bounds supplies a general method to calculate the many-body density of states in high-dimensional irreducible sectors for arbitrary interacting Hamiltonians. The same construction yields rigorous bounds on the ground-state energy in each sector and enables evaluation of microcanonical observables throughout the spectrum. The framework is shown to identify quantum phase transitions and excited-state quantum phase transitions in the Lipkin-Meshkov-Glick model across spin sectors and to produce a highest-spin-sector density of states for the ferromagnetic transverse-field Ising chain with power-law 1/r^

What carries the argument

The generalized coherent state formalism applied to irreducible symmetry sectors, combined with Simon-Lieb bounds that control the quantum partition function and thereby determine the density of states.

Load-bearing premise

That the generalized coherent-state formalism together with Simon-Lieb bounds can be applied to arbitrary interacting Hamiltonians while still producing usefully tight bounds and accurate density of states in high-dimensional irreducible sectors.

What would settle it

Exact diagonalization of a small interacting spin system in a high-dimensional irreducible sector; if the resulting density of states or ground-state energy differs substantially from the values obtained via the coherent-state plus Simon-Lieb construction, the framework does not hold.

Figures

Figures reproduced from arXiv: 2604.14367 by Deniz Coskun, R. Chitra.

Figure 1
Figure 1. Figure 1: FIG. 1. Lower and upper bounds for the ground state energy [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a)The ESQP-Diagram of the LMG-Model. For the DOS calculations we have fixed [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Microcanonical expectation values for spin observ [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

We develop a general framework to calculate the many-body density of states (DOS) of isolated and interacting quantum systems. Based on the generalized coherent state formalism and the Simon-Lieb bounds for a quantum partition function, our method provides a general method of calculation for the DOS in high-dimensional irreducible sectors. This framework further provides rigorous bounds for the ground state energy in each sector and enables the calculation of microcanonical observables across the entire spectrum. Using the Lipkin-Meshkov-Glick (LMG) model as a test bed, we validate our framework by successfully identifying quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs) across spin sectors. Unlike existing model-specific numerical or analytical techniques, our formalism relies on general underlying symmetries, making it broadly applicable. Applying our method to the ferromagnetic transverse field Ising chain with power law interactions, we demonstrate that its highest-spin-sector DOS is qualitatively identical to that of LMG-type Hamiltonians. Our work establishes a versatile and computationally efficient bridge between algebraic structure and many-body thermodynamics.

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 / 0 minor

Summary. The manuscript develops a generalized coherent state framework combined with Simon-Lieb bounds to compute the many-body density of states (DOS) for isolated interacting quantum systems, with emphasis on high-dimensional irreducible sectors. It claims to deliver rigorous ground-state energy bounds per sector and microcanonical observables across the spectrum. Validation is performed on the LMG model (identifying QPTs and ESQPTs across spin sectors) and the ferromagnetic power-law Ising chain (showing qualitative DOS similarity to LMG-type models). The approach is positioned as symmetry-based and broadly applicable rather than model-specific.

Significance. If the central derivations hold and the bounds prove sufficiently tight, the work would supply a computationally efficient, symmetry-leveraging route to many-body thermodynamics and DOS that bridges algebraic structure with observables, including rigorous energy bounds. This could complement existing numerical methods for systems with suitable symmetries.

major comments (2)
  1. [Abstract] Abstract and method overview: The claim that the framework provides a 'general method of calculation for the DOS in high-dimensional irreducible sectors' for arbitrary interacting Hamiltonians rests on the applicability of Simon-Lieb bounds. These bounds classically require ferromagnetic or positive-interaction conditions to produce usefully tight estimates on the partition function; for generic (e.g., antiferromagnetic or frustrated) cases the inequalities either fail or yield bounds too loose for reliable Laplace inversion into DOS(E). The manuscript validates only on LMG (all-to-all ferromagnetic) and power-law ferromagnetic Ising, leaving the generality claim unsupported.
  2. [Validation on LMG and Ising models] Validation section (LMG and Ising results): The abstract asserts 'successful identification of QPTs and ESQPTs' and 'qualitative agreement' but supplies no derivation details, error estimates, quantitative comparison to exact diagonalization or other benchmarks, or discussion of bound tightness. Without these, it is impossible to assess whether the DOS reproduces the claimed phase-transition signatures with sufficient accuracy to support the microcanonical-observable claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the major comments point by point below, acknowledging where the manuscript requires clarification or additional material, and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract and method overview: The claim that the framework provides a 'general method of calculation for the DOS in high-dimensional irreducible sectors' for arbitrary interacting Hamiltonians rests on the applicability of Simon-Lieb bounds. These bounds classically require ferromagnetic or positive-interaction conditions to produce usefully tight estimates on the partition function; for generic (e.g., antiferromagnetic or frustrated) cases the inequalities either fail or yield bounds too loose for reliable Laplace inversion into DOS(E). The manuscript validates only on LMG (all-to-all ferromagnetic) and power-law ferromagnetic Ising, leaving the generality claim unsupported.

    Authors: We agree that the Simon-Lieb bounds, as used in the derivation, are formulated for systems with ferromagnetic (or more generally, positive-semidefinite interaction) couplings and do not hold with the same tightness for arbitrary antiferromagnetic or frustrated Hamiltonians. The manuscript's claim of a 'general method' is intended to emphasize the symmetry-based coherent-state approach that applies to any Hamiltonian possessing suitable irreducible representations, but the subsequent use of Simon-Lieb bounds to obtain the DOS does restrict the practical scope. We will revise the abstract, introduction, and conclusions to explicitly state that the framework yields rigorous DOS bounds and microcanonical observables for Hamiltonians satisfying the conditions under which the Simon-Lieb inequalities are valid (e.g., ferromagnetic interactions). The validation examples were chosen precisely because they meet these conditions and permit direct comparison with exact results; we do not claim applicability beyond this regime without further bounds. revision: yes

  2. Referee: [Validation on LMG and Ising models] Validation section (LMG and Ising results): The abstract asserts 'successful identification of QPTs and ESQPTs' and 'qualitative agreement' but supplies no derivation details, error estimates, quantitative comparison to exact diagonalization or other benchmarks, or discussion of bound tightness. Without these, it is impossible to assess whether the DOS reproduces the claimed phase-transition signatures with sufficient accuracy to support the microcanonical-observable claim.

    Authors: We accept that the current validation section is insufficiently quantitative. In the revised manuscript we will add: (i) explicit step-by-step derivation of the DOS from the coherent-state partition function and Simon-Lieb bounds, including the Laplace-inversion procedure; (ii) direct numerical comparisons of the computed DOS against exact diagonalization for small system sizes (N ≤ 20) in both the LMG and Ising cases, with tabulated relative errors and discussion of bound tightness as a function of temperature and sector dimension; (iii) quantitative metrics (e.g., location and height of DOS peaks or specific-heat singularities) demonstrating that the identified QPT and ESQPT signatures remain accurate within the reported error bars; and (iv) a brief analysis of how the microcanonical observables extracted from the DOS compare with canonical results in the thermodynamic limit. These additions will be placed in a new subsection of the validation section together with supplementary figures. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation builds on external bounds and symmetries.

full rationale

The paper's central method combines the generalized coherent state formalism with Simon-Lieb bounds on the partition function to obtain DOS estimates, ground-state energy bounds, and microcanonical observables in high-dimensional sectors. These ingredients are drawn from independent prior literature on inequalities and algebraic techniques rather than being defined in terms of the target DOS or fitted to the outputs. Validation on the LMG model and power-law Ising chain illustrates applicability where interaction conditions hold but does not substitute for or circularly define the general framework. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of the generalized coherent-state formalism and the Simon-Lieb bounds to general interacting quantum systems; no free parameters or new entities are mentioned in the abstract.

axioms (2)
  • standard math Simon-Lieb bounds for a quantum partition function
    Invoked to obtain rigorous bounds on ground-state energy in each sector.
  • domain assumption Generalized coherent state formalism
    Used as the basis for calculating the density of states in high-dimensional irreducible sectors.

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