Quantum phase transition between symmetry enriched topological phases in tensor-network states

• URL: http://arxiv.org/abs/2305.02432v2
• Date: Mon, 4 Sep 2023 17:18:28 GMT
• Title: Quantum phase transition between symmetry enriched topological phases in tensor-network states
• Authors: Lukas Haller, Wen-Tao Xu, Yu-Jie Liu, Frank Pollmann
• Abstract summary: Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. We propose a tensor-network solvable model that allows us to tune between different symmetry enriched topological (SET) phases.
• Score: 6.014569675344553
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. In this work, we propose a tensor-network solvable model that allows us to tune between different symmetry enriched topological (SET) phases. Concretely, we consider a decorated two-dimensional toric code model for which the ground state can be expressed as a two-dimensional tensor-network state with bond dimension $D=3$ and two tunable parameters. We find that the time-reversal (TR) symmetric system exhibits three distinct phases (i) an SET toric code phase in which anyons transform non-trivially under TR, (ii) a toric code phase in which TR does not fractionalize, and (iii) a topologically trivial phase that is adiabatically connected to a product state. We characterize the different phases using the topological entanglement entropy and a membrane order parameter that distinguishes the two SET phases. Along the phase boundary between the SET toric code phase and the toric code phase, the model has an enhanced $U(1)$ symmetry and the ground state is a quantum critical loop gas wavefunction whose squared norm is equivalent to the partition function of the classical $O(2)$ model. By duality transformations, this tensor-network solvable model can also be used to describe transitions between SET double-semion phases and between $\mathbb{Z}_2\times\mathbb{Z}_2^T$ symmetry protected topological phases in two dimensions.

Related papers

• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  The interplay between symmetry and topological properties plays a very important role in modern physics. How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• Two-dimensional symmetry-protected topological phases and transitions in open quantum systems [0.07673339435080445]
  We investigate the influence of local decoherence on a symmetry-protected topological SPT phase of the two-dimensional (2D) cluster state. We show a topological phase transition of a $mathbbZ(0)timesmathbbZ_2(1)$ SPT phase into the trivial phase occurring at a finite decoherence strength.
  arXiv  Detail & Related papers  (2023-11-21T14:05:48Z)
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping [45.873301228345696]
  localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) propto r-2$ is not resolved yet. We show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions there exist two distinguishable phases at weak and strong disorder.
  arXiv  Detail & Related papers  (2022-05-29T16:53:20Z)
• Topological correlations in three dimensional classical Ising models: an exact solution with a continuous phase transition [8.83889166043817]
  We study a 3D classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases.
  arXiv  Detail & Related papers  (2022-02-23T04:22:30Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Unsupervised Learning of Symmetry Protected Topological Phase Transitions [0.0]
  In particular, we show that the phase transitions associated with these phases can be detected in different bosonic and fermionic models in one dimension. Our approach serves as an inexpensive computational method for detecting topological phases transitions associated with SPT systems.
  arXiv  Detail & Related papers  (2021-11-16T19:34:16Z)
• Quantum phase transition in the one-dimensional Dicke-Hubbard model with coupled qubits [20.002319486166016]
  We study the ground state phase diagram of a one-dimensional two qubits Dicke-Hubbard model with XY qubit-qubit interaction.
  arXiv  Detail & Related papers  (2021-11-05T13:17:49Z)
• Quantum correlations, entanglement spectrum and coherence of two-particle reduced density matrix in the Extended Hubbard Model [62.997667081978825]
  We study the ground state properties of the one-dimensional extended Hubbard model at half-filling. In particular, in the superconducting region, we obtain that the entanglement spectrum signals a transition between a dominant singlet (SS) to triplet (TS) pairing ordering in the system.
  arXiv  Detail & Related papers  (2021-10-29T21:02:24Z)
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer [0.0]
  We show that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled $mathbbZtimesmathbbZ$ and the strongly-coupled $mathbbZ$ can be described by the condensation of bosonic quasiparticles from both sides.
  arXiv  Detail & Related papers  (2020-10-12T19:16:36Z)
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase [0.0]
  We find a corresponding quantum model constructed by applying a local invertible transformation on a d-level version of Kitaev's Toric code. We identify an extended topological phase transition in our model in a sense that, for $d geq 5$, a KT-like quantum phase emerges between a $Z_d$ topological phase and a trivial phase.
  arXiv  Detail & Related papers  (2020-04-30T10:16:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.