Topological quantum phase transitions in 2D isometric tensor networks
- URL: http://arxiv.org/abs/2312.05079v2
- Date: Tue, 30 Jan 2024 17:04:58 GMT
- Title: Topological quantum phase transitions in 2D isometric tensor networks
- Authors: Yu-Jie Liu, Kirill Shtengel, Frank Pollmann
- Abstract summary: We introduce a procedure to construct isoTNS-solvable models in 2D.
We illustrate this by constructing an isoTNS path with bond dimension $D = 2$ interpolating between distinct symmetry-enriched topological phases.
We provide an exact linear-depth parametrized local quantum circuit that realizes the path and therefore it can be efficiently realized on a programmable quantum device.
- Score: 4.189204855014776
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Isometric tensor networks (isoTNS) form a subclass of tensor network states
that have an additional isometric condition, which implies that they can be
efficiently prepared with a linear-depth sequential quantum circuit. In this
work, we introduce a procedure to construct isoTNS-solvable models in 2D. By
continuously tuning a parameter in the isoTNS, the many-body ground state
undergoes quantum phase transitions, exhibiting distinct 2D quantum phases. We
illustrate this by constructing an isoTNS path with bond dimension $D = 2$
interpolating between distinct symmetry-enriched topological (SET) phases. At
the transition point, the isoTNS wavefunction is related to a gapless point in
the classical six-vertex model. Furthermore, the critical wavefunction supports
a power-law correlation along one spatial direction while remains long-range
ordered in the other spatial direction. We provide an exact linear-depth
parametrized local quantum circuit that realizes the path and therefore it can
be efficiently realized on a programmable quantum device.
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