Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state

TL;DR

This paper demonstrates the first successful use of thermal pure matrix product states in two dimensions to accurately simulate the thermal equilibrium of the Kitaev honeycomb model across a wide temperature range, capturing complex quantum phenomena.

Contribution

It introduces a TPQ-MPS framework for 2D systems that efficiently reproduces thermodynamic features and topological states, reducing computational costs compared to traditional methods.

Findings

Successfully reproduces specific-heat peaks of the Kitaev model

Captures emergent Majorana fermions and gauge fields

Approaches the exact ground state with finite-size clusters

Abstract

We present the first successful application of the matrix product state (MPS) representing a thermal quantum pure state (TPQ) in equilibrium in two spatial dimensions over almost the entire temperature range. We use the Kitaev honeycomb model as a prominent example hosting a quantum spin liquid (QSL) ground state to target the two specific-heat peaks previously solved nearly exactly using the free Majorana fermionic description. Starting from the high-temperature random state, our TPQ-MPS framework on a cylinder precisely reproduces these peaks, showing that the quantum many-body description based on spins can still capture the emergent itinerant Majorana fermions in a ${\mathbb Z}_2$ gauge field. The truncation process efficiently discards the high-energy states, eventually reaching the long-range entangled topological state approaching the exact ground state for a given finite size cluster. An advantage of TPQ-MPS over exact diagonalization or purification-based methods is its lowered numerical cost coming from a reduced effective Hilbert space even at finite temperature.