Thermal Tensor Network Simulations of Lattice Fermions with Fixed Filling

TL;DR

This paper introduces a fixed-particle-number tensor network method for simulating finite-temperature properties of lattice fermions, improving stability and efficiency in studying correlated electron systems.

Contribution

It develops a fixed-$N$ tanTRG algorithm that stabilizes particle number during thermal simulations, enabling more accurate finite-temperature studies of fermionic models.

Findings

Successfully benchmarks on free fermions

Analyzes charge and spin correlations in the Hubbard model

Identifies temperature scales for stripe formation

Abstract

Numerical simulations of strongly correlated fermions at finite temperature are essential for studying high-temperature superconductivity and other quantum many-body phenomena. The recently developed tangent-space tensor renormalization group (tanTRG) provides an efficient and accurate framework by representing thermal density operators as matrix product operators. However, the particle number generally varies during the cooling process. The conventional strategy of fine-tuning chemical potentials to reach a target filling is computationally demanding. Here we propose a fixed-$N$ tanTRG algorithm that stabilizes the average particle number by adaptively tuning the chemical potential within the imaginary-time evolution. We benchmark its accuracy on exactly solvable free fermions, and further apply it to the square-lattice Hubbard model. For hole-doped cases, we study the temperature evolution of charge and spin correlations, identifying several characteristic temperature scales for stripe formation. Our results establish fixed-$N$ tanTRG as an efficient and reliable tool for finite-temperature studies of correlated fermion systems.