Signatures of quantum criticality in the complex inverse temperature plane

Abstract

Concepts of the complex partition functions and the Fisher zeros provide intrinsic statistical mechanisms for finite temperature and real time dynamical phase transitions. We extend the utility of these complexifications to quantum phase transitions. We exactly identify different Fisher zeros on lines or closed curves and elucidate their correspondence with domain-wall excitations or confined mesons for the one-dimensional transverse field Ising model. The crossover behavior of the Fisher zeros provides a fascinating picture for criticality near the quantum phase transition, where the excitation energy scales are quantitatively determined. We further confirm our results by tensor network calculations and demonstrate a clear signal of deconfined meson excitations from the disruption of the closed zero curves. Our results unambiguously show significant features of Fisher zeros for a quantum phase transition and open up a new route to explore quantum criticality.

6 pages, 5 figures

References in corpus (8)

• "Deconfined" quantum critical points
• Observation of Lee-Yang zeros
• Observation of E8 Particles in an Ising Chain Antiferromagnet
• Experimental Observation of Quantum Many-Body Excitations of $E_8$ Symmetry in the Ising Chain Ferromagnet CoNb${}_2$O${}_6$
• Lines of Fisher's zeros as separatrices for complex renormalization group flows
• Variational corner transfer matrix renormalization group method for classical statistical models
• Characterizing Superradiant Phase of the Quantum Rabi Model
• Symmetry-protected topological phase transitions and robust chiral order on a tunable zigzag lattice

Cited by in corpus (4)

• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Detecting Many-Body Scars from Fisher Zeros
• Many-body computing on Field Programmable Gate Arrays