Higher Berry Connection for Matrix Product States

• URL: http://arxiv.org/abs/2405.05327v1
• Date: Wed, 8 May 2024 18:00:33 GMT
• Title: Higher Berry Connection for Matrix Product States
• Authors: Shuhei Ohyama, Shinsei Ryu,
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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