arXiv:2509.02185 · Journal of High Energy Physics

Tensor renormalization group approach to entanglement entropy

Takahiro Hayazaki, Daisuke Kadoh, Shinji Takeda, Gota Tanaka

Published Mar 2, 2026• 0 citations

Abstract

A bstract We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a d -dimensional quantum system is represented as a ( d + 1)-dimensional tensor network. We develop an explicit algorithm for d = 1 that enables the calculation of EE for single-interval subsystems of arbitrary size. We test our method in two-dimensional tensor network of the Ising model. The central charge is obtained as c = 0 . 49997(8) for D = 96, which agrees with the theoretical prediction within an error, demonstrating the accuracy and reliability of our proposed method.

DOI: 10.1007/jhep03(2026)002

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arXiv:2509.02185 · Journal of High Energy Physics

Tensor renormalization group approach to entanglement entropy

Takahiro Hayazaki, Daisuke Kadoh, Shinji Takeda, Gota Tanaka

Published Mar 2, 2026• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.1007/jhep03(2026)002

Related papers

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arXiv:2407.14226Physical review. D/Physical review. D.Nov 4, 20243 citations

We report on tensor renormalization group calculations of entanglement entropy in one-dimensional quantum systems. The reduced density matrix of a Gibbs state can be represented as a

1 + 1

-dimensional tensor network, which is analogous to the tensor network representation of the partition function. The HOTRG method is used to approximate the reduced density matrix for arbitrary subsystem sizes, from which we obtain the entanglement entropy. We test our method in the quantum Ising model and obtain the entanglement entropy of the ground state by taking the size of time direction to infinity. The central charge

c

is obtained as

c = 0.49997(8)

for a bond dimension

D_\text{cut}=96

, which agrees with the theoretical value

c=1/2

within the error.

\mathcal {O}(d^2\log (L)\chi ^6)

, with the largest intermediate tensor size of

\mathcal {O}(\chi ^4)

, where d is the lattice dimension, L is the linear size of each lattice axis, and

\chi

is the cutoff of the number of lattice edge states. To validate our algorithm, we conducted numerical experiments on a Gaussian field model, for which the exact free energy is computable in any lattice dimensions. The results demonstrate that the tt-lattice method can calculate the free energy with reasonable accuracy even for a 10D lattice model with modern computational architectures.