Quantum phase transition and critical behavior between the gapless topological phases

Abstract

The phase transition between gapped topological phases represents a class of unconventional criticality beyond the Landau paradigm. However, recent research has shifted attention to topological phases without a bulk gap, where the phase transitions between them are still elusive. In this work, based on large-scale density matrix renormalization group techniques, we investigate the critical behaviors of the extended quantum XXZ model obtained by the Kennedy-Tasaki transformation. Using fidelity susceptibility as a diagnostic, we obtain a complete phase diagram, which includes both topological nontrivial and trivial gapless phases. Furthermore, as the XXZ-type anisotropy parameter $\Delta$ varies, both the critical points $h_c$ and correlation length exponent $\nu$ remain the same as in the $\Delta =0$ case, characterized by $c=3/2$ (Ising + free boson) conformal field theory. Our results indicate that fidelity susceptibility can effectively detect and reveal a stable unconventional critical line between the topologically distinct gapless phases for general $\Delta$. This work serves as a valuable reference for further research on phase transitions within the gapless topological phase of matter.

10 pages, 11 figures. Any comments or suggestions are welcome!

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• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Topological edge states at Floquet quantum criticality
• Quantum entanglement of fermionic symmetry-enriched quantum critical points in one dimension
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Gapless higher-order topology and corner states in Floquet systems
• Gauge theory and mixed state criticality
• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• Incommensurate gapless ferromagnetism connecting competing symmetry-enriched deconfined quantum phase transitions
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• The global phase diagram of the cluster-XY spin chain with dissipation
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Emergent gapless spiral phases and conformal Lifshitz criticality in the cluster Ising model with off-diagonal interactions
• Anomalous Dynamical Scaling at Topological Quantum Criticality
• Topologically nontrivial multicritical points