Multi-critical Behavior in Topological Phase Transitions

Abstract

Topological phase transitions can be described by the theory of critical phenomena and identified by critical exponents that define their universality classes. This is a consequence of the existence of a diverging length at the transition that has been identified as the penetration depth of the surface modes in the non-trivial topological phase. In this paper, we characterize different universality classes of topological transitions by determining their correlation length exponents directly from numerical calculations of the penetration length of the edge modes as a function of the distance to the topological transition. We consider generalizations of the topological non-trivial Su-Schrieefer-Heeger (SSH) model, for the case of next nearest neighbors hopping and in the presence of a synthetic potential. The latter allows the system to transit between two universality classes with different correlation length and dynamic critical exponents. It presents a multi-critical point in its phase diagram since the behavior of the Berry connection depends on the path it is approached. We compare our results with those obtained from a scaling approach to the Berry connection.

1) Improvements in figures 2 and 3. 2) To compare our results with previous works, we added a little sentence in the final of the page 10

References in corpus (19)

• Topological Insulators
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• New directions in the pursuit of Majorana fermions in solid state systems
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Majorana Fermions and Topology in Superconductors
• Topological phases of generalized Su-Schrieffer-Heeger models
• Lifshitz transitions, type-II Dirac and Weyl fermions, event horizon and all that
• Correlation Length, Universality Classes, and Scaling Laws Associated with Topological Phase Transitions
• Universality classes of topological phase transitions with higher-order band crossing
• Universalities of thermodynamic signatures in topological phases
• Weakly Interacting Topological Insulators: Quantum Criticality and Renormalization Group Approach
• Coherent Oscillations and Giant Edge Magnetoresistance in Singly Connected Topological Insulators
• Thermodynamic signatures of edge states in topological insulators
• Renormalization group approach to a $p$-wave superconducting model
• Renormalization group approach to symmetry protected topological phases
• Topological depletions and sub-leading scalings across topological phase transitions
• Finite Size Effects in Topological Quantum Phase Transitions

Cited by in corpus (26)

• Unconventional scaling at non-Hermitian critical points
• Generating quantum multi-criticality in topological insulators by periodic driving
• Topological and non-topological features of generalized Su-Schrieffer-Heeger models
• Characterizing quantum criticality and steered coherence in the XY-Gamma chain
• Fidelity susceptibility near topological phase transitions in quantum walks
• Multi-critical topological transition at quantum criticality
• Unification of topological invariants in Dirac models
• Topology of many-body edge and extended quantum states in an open spin chain: 1/3--plateau, Kosterlitz-Thouless transition, and Luttinger liquid
• Signatures of topological phase transition on a quantum critical line
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• A supervised learning algorithm for interacting topological insulators based on local curvature
• Global entanglement in a topological quantum phase transition
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• Structural disorder-induced topological phase transitions in quasicrystals
• Ground-state phase diagram and thermodynamics of coupled trimer chains
• Topological phase transition between non-high symmetry critical phases and curvature function renormalization group
• Multicriticality in a one-dimensional topological band insulator
• Curvature function renormalisation, topological phase transitions and multicriticality
• Critical and non critical non-Hermitian topological phase transitions in one dimensional chains
• Scaling behavior in a multicritical one-dimensional topological insulator
• Thermodynamics of a Higher-Order Topological Insulator
• Unconventional quantum criticality in a non-Hermitian extended Kitaev chain
• Model studies of topological phase transitions in materials with two types of magnetic atoms
• Effects of anisotropic correlations in fermionic zero-energy bound states of topological phases
• Topological analysis of the complex SSH model using the quantum geometric tensor
• Topologically nontrivial multicritical points