Phase transitions in the ${\mathbb{Z}}_p$ and U(1) clock models

Abstract

Quantum phase transitions are studied in the non-chiral $p$-clock chain, and a new explicitly U(1)-symmetric clock model, by monitoring the ground-state fidelity susceptibility. For $p\ge 5$, the self-dual ${\mathbb{Z}}_p$-symmetric chain displays a double-hump structure in the fidelity susceptibility with both peak positions and heights scaling logarithmically to their corresponding thermodynamic values. This scaling is precisely as expected for two Beresinskii-Kosterlitz-Thouless (BKT) transitions located symmetrically about the self-dual point, and so confirms numerically the theoretical scenario that sets $p=5$ as the lowest $p$ supporting BKT transitions in ${\mathbb{Z}}_p$-symmetric clock models. For our U(1)-symmetric, non-self-dual minimal modification of the $p$-clock model we find that the phase diagram depends strongly on the parity of $p$ and only one BKT transition survives for $p\ge 5$. Using asymptotic calculus we map the self-dual clock model exactly, in the large $p$ limit, to the quantum $O(2)$ rotor chain. Finally, using bond-algebraic dualities we estimate the critical BKT transition temperatures of the classical planar $p$-clock models defined on square lattices, in the limit of extreme spatial anisotropy. Our values agree remarkably well with those determined via classical Monte Carlo for isotropic lattices. This work highlights the power of the fidelity susceptibility as a tool for diagnosing the BKT transitions even when only discrete symmetries are present.

arXiv comment17 pages, 14 figures

References in corpus (36)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Fidelity approach to quantum phase transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Universal Window for Two Dimensional Critical Exponents
• Dualities and the phase diagram of the $p$-clock model
• Algebraic Approach to Interacting Quantum Systems
• The Bond-Algebraic Approach to Dualities
• Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions
• Probability-Changing Cluster Algorithm for Two-Dimensional XY and Clock Models
• Universality away from critical points in two-dimensional phase transitions
• Unified approach to Quantum and Classical Dualities
• The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Fidelity susceptibility of the quantum Ising model in the transverse field: The exact solution
• Response to a twist on systems with Zp symmetry
• Phase transition of the q-state clock model: duality and tensor renormalization
• Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of $q$-state clock models
• Numerical study of the phase transitions in the two-dimensional Z(5) vector model
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump
• Commensurate and Incommensurate States of Topological Quantum Matter
• Spectral function and fidelity susceptibility in quantum critical phenomena
• Current fidelity susceptibility and conductivity in one-dimensional lattice models with open and periodic boundary conditions
• Two leg quantum Ising ladder: A bosonization study of the ANNNI model
• Virasoro Characters from Bethe Equations for the Critical Ferromagnetic Three-State Potts Model
• Berezinskii-Kosterlitz-Thouless transitions in the six-state clock model
• Helical multiferroics for electric field controlled quantum information processing
• Vortex-hole duality: a unified picture of weak and strong-coupling regimes of bosonic ladders with flux
• DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model
• Numerical studies of ground state fidelity of the Bose-Hubbard model
• Topological quasi-one-dimensional state of interacting spinless electrons
• Exact asymptotic correlation functions of bilinear spin operators of the Heisenberg antiferromagnetic spin-$\frac{1}{2}$ chain

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