Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing

• URL: http://arxiv.org/abs/2407.19780v2
• Date: Fri, 18 Oct 2024 07:42:10 GMT
• Title: Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing
• Authors: Huan Yuan, Jinyi Zhang, Shuai Chen, Xiaotian Nie,
• Abstract summary: Kibble-Zurek (KZ) mechanism describes the scaling behavior when driving a system across a continuous symmetry-breaking transition. Previous studies have shown that the KZ-like scaling behavior also lies in the topological transitions in the Qi-Wu-Zhang model (2D) and the Su-Schrieffer-Heeger model (1D)
• Score: 3.5964577257298522
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kibble-Zurek (KZ) mechanism describes the scaling behavior when driving a system across a continuous symmetry-breaking transition. Previous studies have shown that the KZ-like scaling behavior also lies in the topological transitions in the Qi-Wu-Zhang model (2D) and the Su-Schrieffer-Heeger model (1D), although symmetry breaking does not exist here. Both models with linear band crossings give that $\nu=1$ and $z=1$. We wonder whether different critical exponents can be acquired in topological transitions beyond linear band crossing. In this work, we look into the KZ behavior in a topological 2D checkerboard lattice with a quadratic band crossing. We investigate from dual perspectives: momentum distribution of the Berry curvature in clean systems for simplicity, and real-space analysis of domain-like local Chern marker configurations in disordered systems, which is a more intuitive analog to conventional KZ description. In equilibrium, we find the correlation length diverges with a power $\nu\simeq 1/2$. Then, by slowly quenching the system across the topological phase transition, we find that the freeze-out time $t_\mathrm{f}$ and the unfrozen length scale $\xi(t_\mathrm{f})$ both satisfy the KZ scaling, verifying $z\simeq 2$. We subsequently explore KZ behavior in topological phase transitions with other higher-order band crossing and find the relationship between the critical exponents and the order. Our results extend the understanding of the KZ mechanism and non-equilibrium topological phase transitions.

Related papers

• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model [0.26107298043931204]
  We study the nontrivial renormalization-group scenario of fixed-point annihilation in spin-boson models. We find a tunable transition between two localized phases that can be continuous or strongly first-order. We also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent.
  arXiv  Detail & Related papers  (2024-03-04T19:00:07Z)
• Quantum chaos in PT symmetric quantum systems [2.2530496464901106]
  We study the interplay between $mathcalPT$-symmetry and quantum chaos in a non-Hermitian dynamical system. We find that the complex level spacing ratio can distinguish between all three phases. In the phases with $mathcalPT$-symmetry, the OTOC exhibits behaviour akin to what is observed in the Hermitian system.
  arXiv  Detail & Related papers  (2024-01-14T06:47:59Z)
• Entanglement phase transition due to reciprocity breaking without measurement or post-selection [59.63862802533879]
  EPT occurs for a system undergoing purely unitary evolution. We analytically derive the entanglement entropy out of and at the critical point for the $l=1$ and $l/N ll 1$ case.
  arXiv  Detail & Related papers  (2023-08-28T14:28:59Z)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\cal{PT}$-symmetry breaking in a Floquet system [3.121345642619774]
  We investigate the dynamics of out-of-time-order correlators (OTOCs) in a non-Hermitian kicked rotor model. In the unbroken phase of $mathcalPT$ symmetry, the OTOCs increase monotonically and eventually saturate with time. Just beyond the phase transition points, the OTOCs increase in the power-laws of time, with the exponent larger than two.
  arXiv  Detail & Related papers  (2023-02-20T06:44:13Z)
• 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)
• 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)
• SYK meets non-Hermiticity II: measurement-induced phase transition [16.533265279392772]
  We analytically derive the effective action in the large-$N$ limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. We also verify the large-$N$ critical exponents by numerically solving the Schwinger-Dyson equation.
  arXiv  Detail & Related papers  (2021-04-16T17:55:08Z)

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.