Tensor product variational formulation applied to pentagonal lattice

TL;DR

This paper applies a tensor product variational approach to study quantum spin models on a hyperbolic lattice, revealing phase transition behavior and ground state energies with novel tensor solutions.

Contribution

It introduces a tensor product variational formulation for hyperbolic lattices and analyzes quantum spin models, providing new insights into their ground states and phase transitions.

Findings

Observed mean-field-like universality of the Ising phase transition.

Calculated variational ground-state energies for the models.

Discovered an exceptional three-parameter solution for the ground state.

Abstract

The uniform two-dimensional variational tensor product state is applied to the transverse-field Ising, XY, and Heisenberg models on a regular hyperbolic lattice surface. The lattice is constructed by tessellation of the congruent pentagons with the fixed coordination number being four. As a benchmark, the three models are studied on the flat square lattice simultaneously. The mean-field-like universality of the Ising phase transition is observed in full agreement with its classical counterpart on the hyperbolic lattice. The tensor product ground state in the thermodynamic limit has an exceptional three-parameter solution. The variational ground-state energies of the spin models are calculated.