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arxiv: 2510.05233 · v2 · submitted 2025-10-06 · ⚛️ nucl-th · cond-mat.quant-gas

Ab initio study of the neutron and Fermi polarons on the lattice

Ryan Curry , Jasmine Kozar , Alexandros Gezerlis This is my paper

Pith reviewed 2026-05-18 08:55 UTC · model grok-4.3

classification ⚛️ nucl-th cond-mat.quant-gas
keywords polaronquantum Monte CarlolatticeFermi polaronneutron polaroncold atomsnuclear physicsimpurity problem
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0 comments X

The pith

Lattice quantum Monte Carlo calculations give benchmark energies for Fermi and neutron polarons.

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

The paper applies auxiliary-field quantum Monte Carlo on a lattice to compute the energy of a fermionic impurity in a sea of spin-polarized fermions. It examines the Fermi polaron at unitarity and across a range of scattering lengths, then turns to the neutron polaron as a constraint on nuclear physics. A parametric matrix model speeds up the tuning of lattice parameters to match two-body energies in a periodic box via Luscher's formula, so that the resulting many-body results can act as reference values for other calculations and measurements.

Core claim

The authors establish that auxiliary-field quantum Monte Carlo on the lattice, with parameters fixed to two-body physics through the parametric matrix model and Luscher's formula, produces reliable energies for the polaron in both cold-atom and nuclear contexts that can serve as stringent benchmarks for future theoretical and experimental work.

What carries the argument

Auxiliary-field quantum Monte Carlo applied to a lattice Hamiltonian for the fermionic polaron, with parameters tuned by the parametric matrix model to reproduce two-body energies in a periodic box according to Luscher's formula.

If this is right

  • The computed polaron energies provide direct reference points for cold-atom experiments across scattering lengths.
  • The neutron polaron results constrain models of neutron-rich matter in nuclear physics.
  • The same lattice framework can be applied to other impurity problems in fermionic systems.
  • Future many-body calculations in both atomic and nuclear regimes can be tested against these lattice results.

Where Pith is reading between the lines

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

  • These benchmarks could help clarify the equation of state in low-density neutron matter by offering an independent lattice anchor.
  • The method's generality suggests it could be extended to study polarons in mixed atomic-nuclear hybrid systems or other tunable interactions.
  • Varying the lattice volume or spacing in follow-up runs would test how well the current tuning suppresses finite-size effects.

Load-bearing premise

Tuning the lattice Hamiltonian parameters to two-body energies via Luscher's formula and the parametric matrix model introduces no uncontrolled discretization or finite-volume errors that propagate into the many-body polaron energies.

What would settle it

A precise experimental measurement or independent exact calculation of the polaron energy at unitarity or for the neutron case that differs significantly from the lattice Monte Carlo value without an identified source of error.

Figures

Figures reproduced from arXiv: 2510.05233 by Alexandros Gezerlis, Jasmine Kozar, Ryan Curry.

Figure 1
Figure 1. Figure 1: FIG. 1. Average percent error of 4x4 PMMs as a function [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Extrapolation to the continuum limit of zero fill [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Energy of the Fermi polaron, in units of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Energy of the Fermi and neutron polaron across a [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Energy of the neutron polaron in units of the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

We have used the auxiliary-field quantum Monte Carlo (AFQMC) many-body approach on the lattice to study the equation of state for a fermionic impurity interacting with a background sea of spin-polarized fermions. The impurity, or polaron, is an interesting system in both cold atomic and nuclear physics. Our approach is general, and we are able to straightforwardly study the polaron across these regimes. We first study the Fermi polaron at unitarity and for a wide range of scattering lengths, comparing against previous theoretical and experimental studies. We then explore the neutron polaron which has been shown to be an important constraint for nuclear physics. We have also employed the recently developed parametric matrix model to emulate AFQMC solutions to the two-body problem on the lattice, to accelerate the tuning of our lattice Hamiltonian parameters directly to two-body energies in a periodic box, following Luscher's formula. Our lattice quantum Monte Carlo results for the polaron in both a cold atomic and nuclear physics context can serve as stringent benchmarks for future theoretical and experimental research.

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 reports an auxiliary-field quantum Monte Carlo (AFQMC) lattice study of the equation of state for a fermionic impurity (polaron) interacting with a spin-polarized Fermi sea. It examines the Fermi polaron at unitarity and across a range of scattering lengths, with comparisons to prior theory and experiment, and extends the method to the neutron polaron. Lattice Hamiltonian parameters are tuned via a parametric matrix model to match two-body energies in a periodic box using Luscher's formula; the resulting many-body energies are presented as benchmarks for cold-atom and nuclear-physics applications.

Significance. If discretization and finite-volume errors are shown to be controlled at the level of the reported precision, the numerical results would constitute useful ab initio benchmarks bridging ultracold atoms and nuclear structure. The generality of the AFQMC lattice framework across regimes and the practical acceleration provided by the parametric matrix model for two-body tuning are clear strengths. The work supplies concrete numerical data rather than a new analytic derivation, which is appropriate for a benchmark-oriented study.

major comments (2)
  1. [Section describing the parametric matrix model and two-body tuning] The central benchmark claim rests on the assumption that tuning the lattice parameters to two-body energies via the parametric matrix model and Luscher's formula introduces no uncontrolled errors that propagate into the many-body polaron energies. No explicit sensitivity analysis or residual-mismatch propagation test is provided for the extracted polaron energies.
  2. [Results section on Fermi and neutron polaron energies] Comparisons to previous theoretical and experimental studies for the Fermi polaron are stated, yet the manuscript does not supply full error budgets, complete data tables, or volume-extrapolation checks. This limits the ability to judge whether the new results achieve the precision needed to serve as stringent benchmarks.
minor comments (2)
  1. [Hamiltonian and parameter definitions] Clarify the notation distinguishing the lattice interaction parameters from the physical scattering length and effective range throughout the text and equations.
  2. [Figures and captions] Ensure all figures displaying polaron energies include explicit error bars, lattice-spacing labels, and volume sizes consistent with the accompanying text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify the presentation of our benchmark results. We address each major comment below and have revised the manuscript to incorporate the requested analyses and supporting data.

read point-by-point responses

  1. Referee: [Section describing the parametric matrix model and two-body tuning] The central benchmark claim rests on the assumption that tuning the lattice parameters to two-body energies via the parametric matrix model and Luscher's formula introduces no uncontrolled errors that propagate into the many-body polaron energies. No explicit sensitivity analysis or residual-mismatch propagation test is provided for the extracted polaron energies.

    Authors: We agree that an explicit sensitivity analysis strengthens the central benchmark claim. In the revised manuscript we have added a dedicated subsection that quantifies the propagation of two-body tuning uncertainties. We vary the lattice interaction parameters within the residual mismatch allowed by the parametric matrix model and Luscher's formula (at the level of the two-body energy precision), recompute the many-body polaron energies on representative volumes, and demonstrate that the induced shifts remain well below the statistical Monte Carlo uncertainties reported for the final results. This test is now included for both the unitary Fermi polaron and the neutron polaron cases. revision: yes

  2. Referee: [Results section on Fermi and neutron polaron energies] Comparisons to previous theoretical and experimental studies for the Fermi polaron are stated, yet the manuscript does not supply full error budgets, complete data tables, or volume-extrapolation checks. This limits the ability to judge whether the new results achieve the precision needed to serve as stringent benchmarks.

    Authors: We acknowledge that the original manuscript presented only selected comparisons and summary figures. The revised version now includes (i) complete tabulated data for the polaron energy at all studied scattering lengths and lattice volumes, (ii) a detailed error budget separating statistical, systematic (including discretization and tuning), and extrapolation uncertainties, and (iii) explicit volume-extrapolation plots and fits for the Fermi polaron at unitarity and selected scattering lengths. The extrapolated infinite-volume values with combined uncertainties are reported and used in the comparisons to prior theory and experiment. The same level of documentation is provided for the neutron polaron results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; self-contained numerical benchmarks

full rationale

The paper calibrates lattice Hamiltonian parameters to two-body energies via Luscher's formula using the parametric matrix model, then computes many-body polaron energies directly with AFQMC. This is explicit external calibration to a standard result (Luscher), not a reduction of the central many-body claim to the fit by construction. No self-citation load-bearing for the benchmark utility, no self-definitional steps, and no renaming or ansatz smuggling. The results are presented as numerical data rather than derived predictions equivalent to inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central results rest on standard many-body Monte Carlo assumptions and a tuning procedure drawn from prior literature; no new entities are postulated.

free parameters (1)
  • lattice interaction parameters
    Tuned via parametric matrix model to match two-body energies in a periodic box
axioms (1)
  • domain assumption Auxiliary-field quantum Monte Carlo accurately samples the fermionic many-body problem without prohibitive sign issues
    Invoked implicitly as the computational engine for the equation of state

pith-pipeline@v0.9.0 · 5716 in / 1178 out tokens · 29424 ms · 2026-05-18T08:55:32.177495+00:00 · methodology

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