Year: 2017
Type: article
Abstract: Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network-and hence the geometry-is largely fixed a priori by the choice of the tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of noninteracting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.
Source: Physical Review Letters
Authors: Katharine Hyatt, James R. Garrison, Bela Bauer
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Quantum entanglement in Many-Body Systems, Graduate Research Fellowship Program (GRFP), Center of Excellence for Materials Research and Innovation at UCSB, Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics, MRI-R2: Acquisition of a high performance central computing facility at UCSB
OpenAlex ID: W2606529432