Lee-Yang theory of quantum phase transitions with neural network quantum states

Abstract

Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.

10 pages, 6 figures, 1 table

References in corpus (13)

• The density-matrix renormalization group in the age of matrix product states
• Observation of Lee-Yang zeros
• Machine learning technique to find quantum many-body ground states of bosons on a lattice
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• Neural-network quantum state tomography
• Lee-Yang zeros and large-deviation statistics of a molecular zipper
• Dense QCD in a Finite Volume
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• Lee-Yang theory of criticality in interacting quantum many-body systems
• Lee-Yang theory of the two-dimensional quantum Ising model
• Solving the nuclear pairing model with neural network quantum states
• Ground state search by local and sequential updates of neural network quantum states

Cited by in corpus (5)

• Lee-Yang theory of the superradiant phase transition in the open Dicke model
• Imaginary-Temperature Zeros for Quantum Phase Transitions
• Fidelity zeros and Lee-Yang theory of quantum phase transitions
• Lee-Yang formalism for phase transitions of interacting fermions using tensor networks
• Hierarchy of percolation patterns in a kinetic replication model