Finite-size scaling at the first-order quantum transitions of quantum Potts chains

Abstract

We investigate finite-size effects in quantum systems at first-order quantum transitions. For this purpose we consider the one-dimensional q-state Potts models which undergo a first-order quantum transition for any q > 4, separating the quantum disordered and ordered phases with a discontinuity in the energy density of the ground state. The low-energy properties around the transition show finite-size scaling, described by general scaling ansatzes with respect to appropriate scaling variables. The size dependence of the scaling variables presents a particular sensitiveness to boundary conditions, which may be considered as a peculiar feature of first-order quantum transitions.

Scaling properties of work fluctuations after quenches near quantum transitions

“…Let us now extend the above analysis to FOQTs. As shown by earlier works [34,53,54], isolated many-body systems at FOQTs develop FSS behaviors as well. However, they significantly depend on the type of boundary conditions, in particular whether they favor one of the phases or they are neutral, giving rise to FSS characterized by exponential or power-law behaviors.…”

“…The DFSS limit is again defined by the large-L limit, keeping ω, τ , and κ fixed. Note that the FOQT scenario based on the avoided crossing of two levels is not realized for any boundary condition [34]: in some cases the energy difference ∆(L) of the lowest levels may even show a power-law dependence on L. However, the scaling variables κ obtained using the corresponding ∆(L) turn out to be appropriate as well [34]. Similarly to CQTs, the emergence of a DFSS after an out-of-equilibrium quench protocol λ 0 → λ is also expected at FOQTs.…”

“…However, they significantly depend on the type of boundary conditions, in particular whether they favor one of the phases or they are neutral, giving rise to FSS characterized by exponential or power-law behaviors. In the following we shall consider Ising systems with boundary conditions that do not favor any of the two magnetized phases, such as periodic and open boundary conditions, which generally lead to exponential FSS laws [34]. We stress that, for peculiar boundary conditions as the antiperiodic ones, the energy difference of the lowest levels obeys a power-law dependence on L, in which case the situation becomes more subtle [34].…”

“…The natural theoretical context where to set up the analysis is the finite-size scaling (FSS) framework, that has been proven to be effective in proximity of any quantum transition. Indeed the emergence of FSS limits has been predicted both for continuous [33] and first-order [34] quantum transitions (CQTs and FOQTs, respectively), as well as in a dynamic FSS context (DFSS), to describe the quantum dynamics of finite-size many-body systems subject to time-dependent perturbations [35,36]. Analogous FSS frameworks have been recently exploited to study quantuminformation based concepts, as entanglement among parts of the system [37,38,33] as well as other indicators of genuine quantum correlations [39,40,41,42,43,44], the fidelity [45,46], and decoherence [47,48,49].…”

Entanglement scaling at first order quantum phase transitions

“…It is worth mentioning that equation (12) is an approximation whereas, in the previous section we had analytic expressions for Δ L and m 0 in equation (6). Actually, in [31], a similar FSS, with non-analytic expressions, is proposed for the Potts chain with a similar convergence. It seems reasonable, thus, to state that for this 1QPT, when we are close to the 2QPT,  is continuous due to finite size effects and that it obeys the scaling ansatz for 1QPT.…”