Universal scaling for the quantum Ising chain with a classical impurity

Abstract

We study finite-size scaling for the magnetic observables of an impurity residing at the end point of an open quantum Ising chain with transverse magnetic field, realized by locally rescaling the field by a factor μ = 1. In the homogeneous chain limit at μ = 1, we find the expected finite-size scaling for the longitudinal impurity magnetization, with no specific scaling for the transverse magnetization. At variance, in the classical impurity limit μ = 0, we recover finite scaling for the longitudinal magnetization, while the transverse one basically does not scale. We provide both analytic approximate expressions for the magnetization and the susceptibility as well as numerical evidences for the scaling behavior. At intermediate values of μ, finite-size scaling is violated, and we provide a possible explanation of this result in terms of the appearance of a second, impurity-related length scale. Finally, by going along the standard quantum-to-classical mapping between statistical models, we derive the classical counterpart of the quantum Ising chain with an end-point impurity as a classical Ising model on a square lattice wrapped on a half-infinite cylinder, with the links along the first circle modified as a function of μ.

Impurity-driven transitions in frustrated quantum Ising rings

“…( 83) and (84). Thus, this situation is in contrast with the OBC case [25], or the AFZM discussed in Sec. .…”

“…Because this tedious mapping is different from that in the case of open boundary condition (OBC) [25], we give some details about the solution of the system. The Hamiltonians, H R/NS , are solved according to the procedure originally stated by Lieb et al [26,27].…”

“…In this work, we investigate a point impurity in the quantum Ising chain seamed with ring frustration. The merit of point impurity is that it is easier to control [24,25]. The intriguing interplay between the ring frustration and the point impurity leads to a rich ground-state phase diagram.…”

Entanglement entropy of a three-spin-interacting spin chain with a time-reversal-breaking impurity at one boundary

“…We hence stress that the impurity is purely quantum in nature. In parallel, the effect of a classical impurity, the zero transverse field at the first site of an otherwise homogeneous chain, has been investigated in a quantum Ising chain by studying the finite size scaling of the magnetizations [63]. The nature of this impurity is classical due to the fact that the left most spin can not flip; in contrary, the impurity term considered in Eq.…”

Lindblad dissipative dynamics in the presence of phase coexistence

“…In this work we shall address right this issue in the prototype quantum first order phase transition displayed by a fully connected quantum Ising model with p-spin exchange, where p > 2. Quantum spin models, besides being paradigmatic systems for studying quantum phase transitions, also constitute a good playground to investigate, both theoretically and experimentally, the driven dissipative dynamics [16][17][18][19][20][21][22][23][24] , including its realization in pertinently designed quantum impurity models realized at junctions of spin chains [25][26][27][28][29] . We shall model the dissipative dynamics of our case study in the framework of Markovian dynamics, through the rather general master equation derived by Lindblad back in 1976 30,31 , but still widely used [32][33][34][35][36][37][38][39] .…”