We consider two-dimensional (d = 2) systems with short-ranged microscopic interactions, where interface unbinding (wetting) transitions occur in the limit of vanishing temperature T .For T = 0 the transition is characterized by non-universal critical properties analogous to those established for thermal wetting transitions in d = 3, albeit with a redefined capillary parameter ω.Within a functional renormalization-group treatment of an effective interfacial model, we compute the finite-temperature phase diagram, exhibiting a line of interface unbinding transitions, terminating at T = 0 with an interfacial quantum-critical point.We identify distinct scaling regimes, reflecting the interplay between quantum and thermal interfacial fluctuations.A crossover line marking the onset of the quantum-critical regime is described by the d = 3 interfacial correlationlength exponent ν || .This potentially opens another way to investigate the non-universal character of ν || .On the other hand, the emergent interfacial quantum-critical regime shows no signatures of non-universality.
We consider two-dimensional (d = 2) systems with short-ranged microscopic interactions, where interface unbinding (wetting) transitions occur in the limit of vanishing temperature T .For T = 0 the transition is characterized by non-universal critical properties analogous to those established for thermal wetting transitions in d = 3, albeit with a redefined capillary parameter ω.Within a functional renormalization-group treatment of an effective interfacial model, we compute the finite-temperature phase diagram, exhibiting a line of interface unbinding transitions, terminating at T = 0 with an interfacial quantum-critical point.We identify distinct scaling regimes, reflecting the interplay between quantum and thermal interfacial fluctuations.A crossover line marking the onset of the quantum-critical regime is described by the d = 3 interfacial correlationlength exponent ν || .This potentially opens another way to investigate the non-universal character of ν || .On the other hand, the emergent interfacial quantum-critical regime shows no signatures of non-universality.
We consider interfacial phenomena accompanying bulk quantum phase transitions in the presence of surface fields. On general grounds we argue that the surface contribution to the system free energy involves a line of singularities characteristic of an interfacial phase transition, occurring below the bulk transition temperature Tc down to T=0. This implies the occurrence of an interfacial quantum critical regime extending into finite temperatures and located within the portion of the phase diagram where the bulk is ordered. Even in situations where the bulk order sets in discontinuously at T=0, the system's behavior at the boundary may be controlled by a divergent length scale if the tricritical temperature is sufficiently low. Relying on an effective interfacial model we compute the surface phase diagram in bulk spatial dimensionality $d\ensuremath{\geqslant}2$ and extract the values of the exponents describing the interfacial singularities in $d\ensuremath{\geqslant}3$.
The global phase diagram of wetting in the two-dimensional Ising model is obtained through the exact calculation of the surface excess free energy. In addition to a surface field for inducing wetting, a surface-coupling enhancement is also included. The wetting transition (of second order) is critical for any finite ratio of surface coupling J_{s} to bulk coupling J, and becomes of first order in the limit J_{s}/J→∞. However, for J_{s}/J≫1, the critical region is exponentially small and is practically invisible to numerical studies. A distinct preasymptotic regime exists in which the transition displays first-order character. In this regime, surprisingly, the surface susceptibility and surface specific heat develop a divergence and show anomalous scaling with an exponent equal to 3/2.
We study the dynamical melting of hot one-dimensional quantum glasses. We focus on quantum glasses that emerge at strong disorder: specifically, many-body localized systems and their critical variants. The latter category includes disordered Ising, Potts, and anyonic chains whose excited-state properties and dynamics can be accessed via real-space renormalization group methods. As disorder is weakened below a critical value these non-thermal quantum glasses melt via a continuous dynamical phase transition into a classical thermal liquid. By accounting for resonant tunneling of energy, we derive and solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow sub-diffusive equilibration dynamics and energy transport, crossing over to ordinary classical diffusion at asymptotically long length scales for critical glasses. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. For non-critical, many-body localized glasses, the crossover scale diverges and subdiffusion persists to the thermodynamic limit. Our approach provides a firm microscopic basis for understanding the generic structure of many-body delocalization transitions in one dimension, and also reveals a general scaling relation among the critical exponents of the transition.
We performed extensive simulations of the random-bond Ising model confined between walls where competitive surface fields act. By properly taking the thermodynamic limit we unambiguously determined wetting transition points of the system, as extrapolation of localization-delocalization transitions of the interface between domains of different orientation driven by the respective fields. The finite-size scaling theory for wetting with short-range fields [E. V. Albano and K. Binder, Phys. Rev. Lett. 109, 036101 (2012)] establishes that the average magnetization of the sample, with critical exponent $\ensuremath{\beta}$, is the proper order parameter for the study of wetting. While the hyperscaling relationship given by $\ensuremath{\gamma}+2\ensuremath{\beta}={\ensuremath{\nu}}_{\ensuremath{\parallel}}+{\ensuremath{\nu}}_{\ensuremath{\perp}}$ requires $\ensuremath{\beta}=1/2$ ($\ensuremath{\gamma}=4, {\ensuremath{\nu}}_{\ensuremath{\parallel}}=3$, and ${\ensuremath{\nu}}_{\ensuremath{\perp}}=2$), the thermodynamic scaling establishes that ${\mathrm{\ensuremath{\Delta}}}_{s}=\ensuremath{\gamma}+\ensuremath{\beta}$, which in contrast requires $\ensuremath{\beta}=0$ (${\mathrm{\ensuremath{\Delta}}}_{s}=4$), where $\ensuremath{\gamma}, {\ensuremath{\nu}}_{\ensuremath{\parallel}}, {\ensuremath{\nu}}_{\ensuremath{\perp}}$, and ${\mathrm{\ensuremath{\Delta}}}_{s}$ are the critical exponents of the susceptibility, the correlation lengths parallel and perpendicular to the interface, and the gap exponent, respectively. So, we formulate a finite-size scaling theory for wetting without hyperscaling and perform numerical simulations that provide strong evidence of hyperscaling violation (i.e., $\ensuremath{\beta}=0$) and a direct measurement of the susceptibility critical exponent $\ensuremath{\gamma}/{\ensuremath{\nu}}_{\ensuremath{\perp}}=2.0\ifmmode\pm\else\textpm\fi{}0.2$, in agreement with theoretical results for the strong fluctuation regime of wetting transitions with quenched noise.
Quantum Phase Transitions Quantum phase transitions, in contrast to temperature-driven critical phenomena, occur due to a competition between different parameters describing the basic interactions of the system. Their specific feature is the quantum character of the critical fluctuations. This implies, through the uncertainty principle, that energy fluctuations and time are coupled. Then at zero temperature time plays a crucial and fundamental role, the static properties being entangled with the dynamics (Continentino, 1994a; Sondhi et al ., 1997; Sachdev, 1999). In this book we are mainly interested in quantum phase transitions that occur in electronic many-body systems and how scaling concepts can be useful to understand their properties close to these transitions (Continentino, 1994a). Even though a similar approach has been used in the case of interacting bosons (Fisher et al ., 1989) the fermionic problem has its own idiosyncrasies and difficulties. For example, there is no natural order parameter associated with the localisation transition in the electronic case, while bosons at zero temperature are either localised or superfluid so that the superfluid order parameter can be used to distinguish between both phases. If the results of the study of quantum phase transitions were restricted to zero temperature, this would be an interesting but purely academic area of research. What is really exciting about this subject is the effect of quantum critical points (QCP) in the finite temperature phase diagram of actual physical systems, even far away from the QCP (Freitas, 2015). As we will show, there is a special line in this phase diagram, the quantum critical trajectory , where the temperature dependence of the thermodynamic and transport properties is governed by the quantum critical exponents, i.e. those associated with the QCP. This and the observed crossover effects induced by temperature in the non-critical side of the phase diagram of a material with a QCP are sufficient to make the study of quantum phase transitions an inevitable subject. We start this chapter by introducing the scaling theory of quantum critical phenomena, since scaling concepts are used throughout this book.
We investigate the impact of quantum and thermal phase fluctuations on the suppression of superconducting order in two-dimensional systems. Within the two-dimensional quantum XY model in the phase representation, where on-site interaction terms govern quantum phase fluctuations, we perform extensive path-integral quantum Monte Carlo simulations. The resulting temperature-interaction phase diagram establishes the presence of a well-defined critical line ending at a quantum critical point at vanishing temperature with no indication of reentrant behavior. We further demonstrate that the resistance above the critical line reproduces the two expected different critical behaviors. For stronger interactions, above the quantum critical point, the system exhibits a crossover to an insulating regime at low temperatures. Finally, Monte Carlo calculations of current-current correlation functions enable us to extract the frequency-dependent conductivity in both superconducting and normal regimes, revealing a finite-frequency response that we attribute to quantum phase fluctuations.