The quantum wetting transition in the one-dimensional transverse-field Ising model with random bonds is studied. Opposite boundary fields are applied at the two ends of the Ising chain. The interface between two domains with oppositely oriented magnetization is localized near the boundary or in the middle of the chain. The wetting transition refers to the phase transition of localization and delocalization of the interface. The tuning parameter
hL is the boundary field at one end, e.g., the left end. At the transition point
hL=hw, the wetting transition occurs. First, we study the wetting transition with one defect bond. It is a first-order transition, and the interface jumps from the left end of the chain to the defect bond at the transition point. Second, we study the wetting transition with two defect bonds and find that the weaker defect bond dominates the phase transition. The wetting transition is still first order, and the interface is localized at the left end of the chain or at the weaker defect bond. Lastly, the random bond case is studied. The random bonds have a rectangular distribution. The wetting transition is still first order. The finite-size effects are studied. The statistics of the transition points and the energy gaps are obtained. We study lattices with sizes
N=100, 150, 200, 250, 300, and 350. The deviation of the phase transition points
hw does not decrease as the lattice size increases. It is argued that the transition point is sample dependent, i.e., the variation in the transition point
hw does not approach zero, even at the thermodynamic limit.
We study the out-of-equilibrium dynamics of one-dimensional quantum Ising models in a transverse field
g, driven by a time-dependent longitudinal field
h across their {\em magnetic} first-order quantum transition at
h=0, for sufficiently small values of
∣g∣. We consider nearest-neighbor Ising chains of size
L with periodic boundary conditions. We focus on the out-of-equilibrium behavior arising from Kibble-Zurek protocols, in which
h is varied linearly in time with time scale
ts, i.e.,
h(t)=t/ts. The system starts from the ground state at
hi≡h(ti)<0, where the longitudinal magnetization
M is negative. Then it evolves unitarily up to positive values of
h(t), where
M(t) becomes eventually positive. We identify several scaling regimes characterized by a nontrivial interplay between the size
L and the time scale
ts, which can be observed when the system is close to one of the many avoided level crossings that occur for
h≥0. In the
L→∞ limit, all these crossings approach
h=0+, making the study of the thermodynamic limit, defined as the limit
L→∞ keeping
t and
ts constant, problematic. We study such limit numerically, by first determining the large-
L quantum evolution at fixed
ts, and then analyzing its behavior with increasing
ts. Our analysis shows that the system switches from the initial state with
M<0 to a positively magnetized state at
h=h∗(ts)>0, where
h∗(ts) decreases with increasing
ts, apparently as
h∗∼1/lnts. This suggests the existence of a scaling behavior in terms of the rescaled time
Ω=tlnts/ts. The numerical results also show that the system converges to a nontrivial stationary state in the large-
t limit, characterized by an energy significantly larger than that of the corresponding homogeneously magnetized ground state.
We present a detailed study of the finite one-dimensional quantum Ising chain in a transverse field in the presence of boundary magnetic fields coupled with the order-parameter spin operator. We consider two magnetic fields located at the boundaries of the chain that have the same strength and that are aligned in the same or in the opposite direction. We derive analytic expressions for the gap in all phases for large values of the chain length L , as a function of the boundary field strength. We also investigate the behaviour of the chain in the quantum ferromagnetic phase for oppositely aligned fields, focusing on the magnet-to-kink transition that occurs at a finite value of the magnetic field strength. At this transition we compute analytically the finite-size crossover functions for the gap, the magnetisation profile, the two-point correlation function, and the density of fermionic modes. As the magnet-to-kink transition is equivalent to the wetting transition in two-dimensional classical Ising models, our results provide new analytic predictions for the finite-size behaviour of Ising systems in a strip geometry at this transition.
We address the out-of-equilibrium dynamics of a many-body system when one of its Hamiltonian parameters is driven across a first-order quantum transition (FOQT). In particular, we consider systems subject to boundary conditions favoring one of the two phases separated by the FOQT. These issues are investigated within the paradigmatic one-dimensional quantum Ising model, at the FOQTs driven by the longitudinal magnetic field h, with boundary conditions that favor the same magnetized phase (EFBC) or opposite magnetized phases (OFBC). We study the dynamic behavior for an instantaneous quench and for a protocol in which h is slowly varied across the FOQT. We develop a dynamic finite-size scaling theory for both EFBC and OFBC, which displays some remarkable differences with respect to the case of neutral boundary conditions. The corresponding relevant timescale shows a qualitative different size dependence in the two cases: it increases exponentially with the size in the case of EFBC, and as a power of the size in the case of OFBC.
We investigate finite-size effects at first-order quantum transitions. For this purpose we consider the one-dimensional q-state quantum Potts chain, in particular with q=10, which undergoes a first-order transition, separating the quantum disordered and ordered phases with a discontinuity in the energy density of the ground state. In agreement with the general theory, around the transition the low-energy properties show finite-size scaling with respect to appropriate scaling variables. Their size dependence is particularly sensitive to boundary conditions, which is a specific feature of first-order quantum transitions. Finally, we also discuss the finite-size behavior of the q-state Potts model (q≥2) at the first-order transitions driven by a parallel magnetic field, occurring in the ferromagnetic phase.
We have studied quantum phase transition induced by a quench in different one-dimensional spin systems. Our analysis is based on the dynamical mechanism which envisages nonadiabaticity in the vicinity of the critical point. This causes spin fluctuation which leads to the random fluctuation of the Berry phase factor acquired by a spin state when the ground state of the system evolves in a closed path. The two-point correlation of this phase factor is associated with the probability of the formation of defects. In this framework, we have estimated the density of defects produced in several one-dimensional spin chains. At the critical region, the entanglement entropy of a block of
L spins with the rest of the system is also estimated which is found to increase logarithmically with
L. The dependence on the quench time puts a constraint on the block size
L. It is also pointed out that the Lipkin-Meshkov-Glick model in point-splitting regularized form appears as a combination of the
XXX model and Ising model with magnetic field in the negative
z axis. This unveils the underlying conformal symmetry at criticality which is lost in the sharp point limit. Our analysis shows that the density of defects as well as the scaling behavior of the entanglement entropy follows a universal behavior in all these systems.