Universal Finite-Size Scaling around Topological Quantum Phase Transitions

Abstract

The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality and find a scaling function, which discriminates between phases with different topological indexes. This function appears to be universal for all five Altland-Zirnbauer symmetry classes with non-trivial topology in one spatial dimension. We obtain an analytic form of the scaling function and compare it with numerical results.

arXiv comment4 pages, 2 figures. Supplement: 2 pages, 1 figure

References in corpus (12)

• Topological Insulators
• Topological insulators and superconductors
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• Entanglement Entropy and Quantum Field Theory
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• New directions in the pursuit of Majorana fermions in solid state systems
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Symmetries, Dimensions, and Topological Insulators: the mechanism behind the face of the Bott clock

Cited by in corpus (19)

• Coherent and dissipative dynamics at quantum phase transitions
• Local and non-local quantum transport due to Andreev bound states in finite Rashba nanowires with superconducting and normal sections
• Majorana bound states in semiconducting nanostructures
• Boundary spin polarization as robust signature of topological phase transition in Majorana nanowires
• Multipartite entanglement after a quantum quench
• Pinning of Andreev bound states to zero energy in two-dimensional superconductor-semiconductor Rashba heterostructures
• Universal fidelity near quantum and topological phase transitions in finite 1D systems
• Universal finite-size amplitude and anomalous entanglement entropy of $z=2$ quantum Lifshitz criticalities in topological chains
• Universal Hall conductance scaling in non-Hermitian Chern insulators
• Finite Size Scaling of Topological Entanglement Entropy
• Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Universal finite size scaling around tricriticality between topologically ordered, SPT, and trivial phases
• Finite Size Scaling at the Topological Transition: Bilinear-Biquadratic Spin-1 Chain
• $Z_3$ and $(\times Z_3{)}^3$ symmetry protected topological paramagnets
• Unveiling chiral states in the XXZ chain: Finite-size scaling probing symmetry-enriched $c=1$ conformal field theories
• Precise determination of critical points of topological phase transitions via shift current in two-dimensional inversion asymmetric insulators
• Ising quantum criticality in Majorana nanowires
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary