Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality

Abstract

The transverse-field $XY$ chain with the long-range interactions was investigated by means of the exact-diagonalization method. The algebraic decay rate $\sigma$ of the long-range interaction is related to the effective dimensionality $D(\sigma )$, which governs the criticality of the transverse-field-driven phase transition at $H=H_c$. According to the large-$N$ analysis, the phase boundary $H_c(\eta )$ exhibits a reentrant behavior within $2<D<3.065\dots$, as the $XY$-anisotropy $\eta$ changes. On the one hand, as for the $D=(2+1)$ and $(1+1)$ short-range $XY$ magnets, the singularities have been determined as $H_c(\eta )-H_c(0)\sim |\eta |$ and $0$, respectively, and the transient behavior around $D\approx 2.5$ remains unclear. As a preliminary survey, setting $(\sigma ,\eta )=(1,0.5)$, we investigate the phase transition by the agency of the fidelity, which seems to detect the singularity at $H=H_c$ rather sensitively. Thereby, under the setting $\sigma =4/3$ ($D=2.5$), we cast the fidelity data into the crossover-scaling formula with the properly scaled $\eta$, aiming to determine the multi-criticality around $\eta =0$. Our result indicates that the multi-criticality is identical to that of the $D=(2+1)$ magnet, and $H_c(\eta )$'s linearity might be retained down to $D>2$.

References in corpus (33)

• Quantum Computing
• Ground state overlap and quantum phase transitions
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Dynamics of Loschmidt echoes and fidelity decay
• Entanglement entropy for the long range Ising chain
• Quantum coherence and uncertainty in the anisotropic XY chain
• Quantum and classical thermal correlations in the XY spin-1/2 chain
• Quantum Critical Scaling of Fidelity Susceptibility
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems
• Criticality and Phase Diagram of Quantum Long-Range $\text{O(N)}$ models
• The boundary between long-range and short-range critical behavior
• Relations between Short Range and Long Range Ising models
• Phase diagram of a 1 dimensional spin-orbital model
• Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit
• Entanglement and fluctuations in the XXZ model with power-law interactions
• The crossover region between long-range and short-range interactions for the critical exponents
• Fidelity and criticality of quantum Ising chain with long-range interactions
• Quasiparticles in quantum spin chains with long-range interactions
• Quantum Kibble-Zurek physics in long-range transverse-field Ising models
• Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models
• Oscillating fidelity susceptibility near a quantum multicritical point
• One-dimensional long-range percolation: a numerical study
• Fidelity susceptibility in the two-dimensional spin-orbit models
• Quantum criticality and excitations of a long-range anisotropic $XY$-chain in a transverse field
• Fidelity susceptibility of the anisotropic $XY$ model: The exact solution
• Quantum phase transition in the spin-anisotropic quantum spherical model
• Effect of long-range interactions on multipartite entanglement in Heisenberg chains
• Renormalization group for the ${\phi }^4$-theory with long-range interaction and the critical exponent $\eta$ of the Ising model
• Multicritical behavior of the fidelity susceptibility for the 2D quantum transverse-field $XY$ model
• Topological transitions in Ising models

Cited by in corpus (1)

• Monte Carlo based techniques for quantum magnets with long-range interactions