Tensor-network study of the 3d $O(2)$ model at non-zero chemical potential and temperature

TL;DR

This paper employs an improved tensor-network approach to simulate the 3D $O(2)$ model at finite chemical potential and temperature, successfully reproducing key physical phenomena and aligning with existing algorithms.

Contribution

It introduces enhancements to the HOTRG method for anisotropic tensors, reducing systematic errors in simulating the 3D $O(2)$ model at non-zero chemical potential and temperature.

Findings

HOTRG results agree with worm algorithm data.

Silver Blaze phenomenon is reproduced at zero temperature.

Temperature dependence of the number density is accurately captured.

Abstract

We present results of tensor-network simulations of the three-dimensional $O(2)$ model at non-zero chemical potential and temperature, which were computed using the higher-order tensor-renormalization-group method (HOTRG). This necessitated enhancements to the HOTRG blocking procedure to reduce the truncation error in the case of anisotropic tensors. Moreover, the construction of the truncated vector spaces was adapted to strongly reduce the effect of systematic errors in the computation of observables using the finite-difference method. Our (improved) HOTRG results for the evolution of the number density with the chemical potential are in agreement with results obtained with the worm algorithm, and both the Silver Blaze phenomenon at zero temperature and the temperature dependence of the number density can be adequately reproduced.