Higher Berry Connection for Matrix Product States

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Ohyama, Shuhei, Ryu, Shinsei
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866916239436152832
author Ohyama, Shuhei
Ryu, Shinsei
author_facet Ohyama, Shuhei
Ryu, Shinsei
contents In one spatial dimension, families of short-range entangled many-body quantum states, parameterized over some parameter space, can be topologically distinguished and classified by topological invariants built from the higher Berry phase -- a many-body generalization of the Berry phase. Previous works identified the underlying mathematical structure (the gerbe structure) and introduced a multi-wavefunction overlap, a generalization of the inner product in quantum mechanics, which allows for the extraction of the higher Berry phase and topological invariants. In this paper, building on these works, we introduce a connection, the higher Berry connection, for a family of parameterized Matrix Product States (MPS) over a parameter space. We demonstrate the use of our formula for simple non-trivial models.
format Preprint
id arxiv_https___arxiv_org_abs_2405_05327
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Higher Berry Connection for Matrix Product States
Ohyama, Shuhei
Ryu, Shinsei
Strongly Correlated Electrons
High Energy Physics - Theory
Mathematical Physics
Quantum Physics
In one spatial dimension, families of short-range entangled many-body quantum states, parameterized over some parameter space, can be topologically distinguished and classified by topological invariants built from the higher Berry phase -- a many-body generalization of the Berry phase. Previous works identified the underlying mathematical structure (the gerbe structure) and introduced a multi-wavefunction overlap, a generalization of the inner product in quantum mechanics, which allows for the extraction of the higher Berry phase and topological invariants. In this paper, building on these works, we introduce a connection, the higher Berry connection, for a family of parameterized Matrix Product States (MPS) over a parameter space. We demonstrate the use of our formula for simple non-trivial models.
title Higher Berry Connection for Matrix Product States
topic Strongly Correlated Electrons
High Energy Physics - Theory
Mathematical Physics
Quantum Physics
url https://arxiv.org/abs/2405.05327