arXiv:2603.09856

Equilibrium Partition Function of Non-Relativistic CFTs in Harmonic Trap

Eunwoo Lee

Published Mar 10, 2026• 0 citations

Abstract

We investigate the equilibrium partition function of non-relativistic conformal field theories in harmonic quantization. We first analyze the hydrodynamic regime and show that, at leading order, the partition function exhibits a universal structure determined by the equation of state: the logarithm of the partition function develops simple poles in $ω^2-Ω_a^2$, where $ω$ is the harmonic trapping frequency and $Ω_a$ are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of $μ/T$, with $μ$ the particle-number chemical potential and $T$ the temperature. We then study the large-angular-momentum limit $Ω_a\toω$. In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in $ω^2-Ω_a^2$, but with a less universal residue depending separately on $μ/T$ and $ω/T$. As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap.

DOI: 10.48550/arxiv.2603.09856

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arXiv:2603.09856

Equilibrium Partition Function of Non-Relativistic CFTs in Harmonic Trap

Eunwoo Lee

Published Mar 10, 2026• 0 citations

arXiv HTML PDF

Abstract

ω^2-Ω_a^2

, where

ω

is the harmonic trapping frequency and

Ω_a

are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of

μ/T

, with

μ

the particle-number chemical potential and

T

the temperature. We then study the large-angular-momentum limit

Ω_a\toω

. In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in

ω^2-Ω_a^2

, but with a less universal residue depending separately on

μ/T

and

ω/T

. As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap.

DOI: 10.48550/arxiv.2603.09856

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ω^2-Ω_a^2

, where

ω

is the harmonic trapping frequency and

Ω_a

are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of

μ/T

, with

μ

the particle-number chemical potential and

T

the temperature. We then study the large-angular-momentum limit

Ω_a\toω

. In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in

ω^2-Ω_a^2

, but with a less universal residue depending separately on

μ/T

and

ω/T

. As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap.

Semi-universality of CFT

_d

entropy at large spin

{b}_{n}

for all

n

in the noninteracting case, as functions of the trapping and rotational frequencies. We also report on the virial coefficients for the angular momentum and associated moment of inertia. Using the

{b}_{n}

coefficients, we analyze the deconfined limit (in which the angular frequency matches the trapping frequency) and derive explicitly the limiting form of the partition function, showing from the thermodynamic standpoint how both the 2D and 3D cases become effectively homogeneous 2D systems. To tackle the virial coefficients in the presence of weak interactions, we implement a coarse temporal lattice approximation and obtain virial coefficients up to third order.