Berlin 2024 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 17: Focus Session: Quantum Interactive Dynamics II (joint session DY/TT)

TT 17.5: Talk

Monday, March 18, 2024, 16:45–17:00, A 151

Topological quantum phase transitions in exact two-dimensional isometric tensor networks — •Yu-Jie Liu¹, Kirill Shtengel², and Frank Pollmann¹ — ¹Technical University of Munich — ²University of California, Riverside

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 quantum circuit. In this work, we introduce a procedure to construct isoTNS encoding of certain 2D classical partition functions. By continuously tuning a parameter in the isoTNS, the many-body ground state undergoes quantum phase transitions, exhibiting distinct 2D topological order. 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 and can be interpreted as a superposition of world lines of random walking particles. 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. The above features can therefore be efficiently realized on a programmable quantum device. At the end, we briefly discuss the possibility of isoTNS paths interpolating between other 2D topological phases.

Keywords: Tensor networks; Quantum circuits; Quantum phase transitions; Random walk