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Tree Tensor Network Simulation of Dynamical Quantum Phase Transitions in the 2D Transverse-Field Ising Model
Xiangyue Zhang1, Dizhou Xie1, Yongqiang Li1
1College of Science, National University of Defense Technology, Changsha 410073, China.
Entropy (Basel, Switzerland)
|May 26, 2026
Summary
Researchers explored 2D dynamical quantum phase transitions (DQPTs) using tree tensor networks. They discovered anomalous DQPTs driven by local spin excitations, distinct from 1D models.
Area of Science:
- Quantum physics
- Condensed matter physics
- Non-equilibrium quantum dynamics
Background:
- Dynamical quantum phase transitions (DQPTs) challenge equilibrium thermodynamics.
- 1D numerical methods like matrix product states (MPS) have advanced DQPT research.
- Exploring 2D DQPTs is hindered by finite-size effects and quasi-1D mappings.
Purpose of the Study:
- To overcome limitations in studying 2D DQPTs.
- To investigate quench dynamics in the 2D transverse-field Ising model (TFIM).
- To utilize tree tensor networks (TTNs) for direct 2D lattice simulations.
Main Methods:
- Employed a tree tensor network (TTN) approach for direct 2D lattice simulations.
- Computed quench dynamics of the 2D transverse-field Ising model (TFIM).
- Extracted the global Loschmidt echo using the TTN architecture.
Main Results:
- Standard DQPTs observed for deep quenches.
- Anomalous dynamical response found for quenches within the ferromagnetic phase.
- Rate function showed sharp peaks, decoupling from the macroscopic order parameter.
- Identified local spin excitations as drivers of 2D DQPTs.
Conclusions:
- Local spin excitations, not domain walls, drive 2D DQPTs.
- TTN approach enables direct simulation of 2D non-equilibrium quantum matter.
- Results provide a baseline for understanding higher-dimensional DQPTs.
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