arXiv subjects

Ettore Vicari

Publications and source records attributed to Ettore Vicari.

At least 109 records · Page 6Linked to original sources

arXiv2017

Dynamic off-equilibrium transition in systems slowly driven across thermal first-order phase transitions

We study the off-equilibrium behavior of systems with short-range interactions driven across a thermal first-order transition, where the dynamics is exponentially slow. We consider a dynamics that starts in the high-T phase at time t = t_i<0 and ends in in the low-T phase at t=t_f>0, with a time-dependent temperature T(t)/T_c \approx 1 - t/t_s, where t_s is the protocol time scale. A general off-equilibrium scaling (OS) behavior emerges in the limit of large t_s. We check it at the first-order transition of the two-dimensional q-state Potts model with q=10 and 20. The numerical results show evidence of a dynamic transition, where the OS functions show a spinodal-like singularity. Therefore, the general mean-field picture valid for systems with long-range interactions is qualitatively recovered, provided the time dependence is appropriately (logarithmically) rescaled.

cond-mat.stat-mech↗

arXiv2016

$θ$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit

We study the large-$N$ scaling behavior of the $θ$ dependence of the ground-state energy density $E(θ)$ of four-dimensional (4D) $SU(N)$ gauge theories and two-dimensional (2D) $CP^{N-1}$ models, where $θ$ is the parameter associated with the Lagrangian topological term. We consider its $θ$ expansion around $θ=0$, $E(θ)-E(0) = {1\over 2}χ\,θ^2 ( 1 + b_2 θ^2 + b_4θ^4 +\cdots)$ where $χ$ is the topological susceptibility and $b_{2n}$ are dimensionless coefficients. We focus on the first few coefficients $b_{2n}$, which parametrize the deviation from a simple Gaussian distribution of the topological charge at $θ=0$. We present a numerical analysis of Monte Carlo simulations of 4D $SU(N)$ lattice gauge theories for $N=3,\,4,\,6$ in the presence of an imaginary $θ$ term. The results provide a robust evidence of the large-$N$ behavior predicted by standard large-$N$ scaling arguments, i.e. $b_{2n}= O(N^{-2n})$. In particular, we obtain $b_2=\bar{b}_2/N^2 + O(1/N^4)$ with $\bar{b}_2=-0.23(3)$. We also show that the large-$N$ scaling scenario applies to 2D $CP^{N-1}$ models as well, by an analytic computation of the leading large-$N$ dependence.

hep-lat↗

arXiv2016

Shape dependence and anisotropic finite-size scaling of the phase coherence of three-dimensional Bose-Einstein condensed gases

We investigate the equilibrium phase-coherence properties of Bose-condensed particle systems, focusing on their shape dependence and finite-size scaling (FSS). We consider three-dimensional (3D) homogeneous systems confined to anisotropic L x L x L_a boxes, below the BEC transition temperature $T_c$. We show that the phase correlations develop peculiar anisotropic FSS for any $T >1, are characterized by a coherence length ξ_a \sim A_t ρ_s/T where A_t is the transverse area and ρ_s is the superfluid density.

cond-mat.quant-gas↗

arXiv2016

Off-equilibrium scaling behaviors driven by time-dependent external fields in three-dimensional O(N) vector models

We consider the dynamical off-equilibrium behavior of the three-dimensional O$(N)$ vector model in the presence of a slowly-varying time-dependent spatially-uniform magnetic field ${\bm H}(t) = h(t)\,{\bm e}$, where ${\bm e}$ is a $N$-dimensional constant unit vector, $h(t)=t/t_s$, and $t_s$ is a time scale, at fixed temperature $T\le T_c$, where $T_c$ corresponds to the continuous order-disorder transition. The dynamic evolutions start from equilibrium configurations at $h_i < 0$, correspondingly $t_i < 0$, and end at time $t_f > 0$ with $h(t_f) > 0$, or vice versa. We show that the magnetization displays an off-equilibrium scaling behavior close to the transition line ${\bm H}(t)=0$. It arises from the interplay among the time $t$, the time scale $t_s$, and the finite size $L$. The scaling behavior can be parametrized in terms of the scaling variables $t_s^κ/L$ and $t/t_s^{κ_t}$, where $κ>0$ and $κ_t > 0$ are appropriate universal exponents, which differ at the critical point and for $T < T_c$. In the latter case, $κ$ and $κ_t$ also depend on the shape of the lattice and on the boundary conditions. We present numerical results for the Heisenberg ($N=3$) model under a purely relaxational dynamics. They confirm the predicted off-equilibrium scaling behaviors at and below $T_c$. We also discuss hysteresis phenomena in round-trip protocols for the time dependence of the external field. We define a scaling function for the hysteresis loop area of the magnetization that can be used to quantify how far the system is from equilibrium.

cond-mat.stat-mech↗

arXiv2016

Phase diagram and multicritical behaviors of mixtures of 3D bosonic gases

We investigate the Bose-Einstein condensation patterns, the critical and multicritical behaviors of three-dimensional mixtures of bosonic gases with short-range density-density interactions. These systems have a global U(1)+U(1) symmetry, as the system Hamiltonian is invariant under independent U(1) transformations acting on each species. In particular, we consider the three-dimensional Bose-Hubbard model for two lattice bosonic gases coupled by an on-site inter-species density-density interaction. We study the phase diagram and the critical behaviors along the transition lines characterized by the Bose-Einstein condensation of one or both species. We present mean-field calculations and numerical finite-size scaling analyses of quantum Monte Carlo data. We also consider multicritical points, close to which it is possible to observe the condensation of both gas components. We determine the possible multicritical behaviors by using field-theoretical perturbative methods. We consider the U(1)+U(1)-symmetric Landau-Ginzburg-Wilson Phi4 theory and determine the corresponding stable fixed points of the renormalization-group flow. The analysis predicts that, in all cases, the multicritical behavior is analogous to the one that would be observed in systems of two identical gases, with an additional Z_2 exchange symmetry.

cond-mat.quant-gas↗

arXiv2015

Off-equilibrium scaling behaviors across first-order transitions

We study off-equilibrium behaviors at first-order transitions (FOTs) driven by a time dependence of the temperature across the transition point Tc, such as the linear behavior T(t)/Tc = 1 - t/ts where ts is a time scale. In particular, we investigate the possibility of nontrivial off-equilibrium scaling behaviors in the regime of slow changes, corresponding to large ts, analogous to those arising at continuous transitions, which lead to the so-called Kibble-Zurek mechanism. We consider the 2D Potts models which provide an ideal theoretical laboratory to investigate issues related to FOTs driven by thermal fluctuations. We put forward general ansatzes for off-equilibrium scaling behaviors around the time t=0 corresponding to Tc. Then we present numerical results for the q=10 and q=20 Potts models. We show that phenomena analogous to the Kibble-Zurek off-equilibrium scaling emerge also at FOTs with relaxational dynamics, when appropriate boundary conditions are considered, such as mixed boundary conditions favoring different phases at the opposite sides of the system, which enforce an interface in the system.

cond-mat.stat-mech↗

arXiv2015

Critical mass renormalization in renormalized phi4 theories in two and three dimensions

We consider the O(N)-symmetric phi4 theory in two and three dimensions and determine the nonperturbative mass renormalization needed to obtain the phi4 continuum theory. The required nonperturbative information is obtained by resumming high-order perturbative series in the massive renormalization scheme, taking into account their Borel summability and the known large-order behavior of the coefficients. The results are in good agreement with those obtained in lattice calculations.

hep-th↗

arXiv2015

Quantum Ising chains with boundary fields

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 behavior 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 magnetization 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 behavior of Ising systems in a strip geometry at this transition.

cond-mat.stat-mech↗

arXiv2015

Relevance of the axial anomaly at the finite-temperature chiral transition in QCD

We investigate the nature of the finite-temperature chiral transition in QCD with two light flavors, in the case of an effective suppression of the the U(1)_A symmetry breaking induced by the axial anomaly, which implies the symmetry breaking U(2)_L X U(2)_R -> U(2)_V, instead of SU(2)_L X SU(2)_R -> SU(2)_V. For this purpose, we perform a high-order field-theoretical perturbative study of the renormalization-group (RG) flow of the corresponding three-dimensional multiparameter Landau-Ginzburg-Wilson Phi4 theory with the same symmetry-breaking pattern. We confirm the existence of a stable fixed point (FP), and determine its attraction domain in the space of the bare quartic parameters. Therefore, the chiral QCD transition might be continuous also if the U(1)_A symmetry is effectively restored at Tc. However, the corresponding universality class differs from the O(4) vector universality class which would describe a continuous transition in the presence of a substantial U(1)_A symmetry breaking at Tc. We estimate the critical exponents of the U(2)_L X U(2)_R -> U(2)_V universality class by computing and analyzing their high-order perturbative expansions. These results are important to discriminate among the different scenarios for the scaling behavior of QCD with two light flavors close to the chiral transition.

hep-lat↗

arXiv2015

Bose-Einstein condensation and critical behavior of two-component bosonic gases

We study Bose-Einstein condensation (BEC) in three-dimensional two-component bosonic gases, characterizing the universal behaviors of the critical modes arising at the BEC transitions. For this purpose, we use field-theoretical (FT) renormalization-group (RG) methods and perform mean-field and numerical calculations. The FT RG analysis is based on the Landau-Ginzburg-Wilson Phi4 theory with two complex scalar fields which has the same symmetry as the bosonic system. In particular, for identical bosons with exchange Z_2,e symmetry, coupled by effective density-density interactions, the global symmetry is Z_2e X U(1) X U(1). At the BEC transition it may break into Z_2,e X Z_2 X Z_2 when both components condense simultaneously, or to U(1) X Z_2 when only one component condenses. This implies different universality classes for the corresponding critical behaviors. Numerical simulations of the two-component Bose-Hubbard model in the hard-core limit support the RG prediction: when both components condense simultaneously, the critical behavior is controlled by a decoupled XY fixed point, with unusual slowly-decaying scaling corrections arising from the on-site inter-species interaction.

cond-mat.stat-mech↗

arXiv2015

Three-dimensional antiferromagnetic CP(N-1) models

We investigate the critical behavior of three-dimensional antiferromagnetic CP(N-1) [ACP(N-1)] models in cubic lattices, which are characterized by a global U(N) symmetry and a local U(1) gauge symmetry. Assuming that critical fluctuations are associated with a staggered gauge-invariant (hermitian traceless matrix) order parameter, we determine the corresponding Landau-Ginzburg-Wilson (LGW) model. For N=3 this mapping allows us to conclude that the three-component ACP(2) model undergoes a continuous transition that belongs to the O(8) vector universality class, with an effective enlargement of the symmetry at the critical point. This prediction is confirmed by a detailed numerical comparison of finite-size data for the ACP(2) and the O(8) vector models. We also present a renormalization-group (RG) analysis of the LGW theories for N>3. We compute perturbative series in two different renormalization schemes and analyze the corresponding RG flow. We do not find stable fixed points that can be associated with continuous transitions.

cond-mat.stat-mech↗

arXiv2015

Quantum transitions driven by one-bond defects in quantum Ising rings

We investigate quantum scaling phenomena driven by lower-dimensional defects in quantum Ising-like models. We consider quantum Ising rings in the presence of a bond defect. In the ordered phase, the system undergoes a quantum transition driven by the bond defect between a magnet phase, in which the gap decreases exponentially with increasing size, and a kink phase, in which the gap decreases instead with a power of the size. Close to the transition, the system shows a universal scaling behavior, which we characterize by computing, either analytically or numerically, scaling functions for the gap, the susceptibility, and the two-point correlation function. We discuss the implications of these results for the nonequilibrium dynamics in the presence of a slowly-varying parallel magnetic field h, when going across the first-order quantum transition at h=0.

cond-mat.stat-mech↗

arXiv2014

Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQT), such as those arising from the presence of a space-dependent external field, which smooths out the typical discontinuities of the low-energy properties. We argue that scaling phenomena develop at the transition region where the external field takes the value corresponding to the FOQT of the homogenous system. We present numerical evidence of such scaling phenomena at the FOQTs of quantum Ising chains, driven by a parallel magnetic field when the system is in the ferromagnetic phase, and at the FOQT of the q-state Potts chain for q>4, driven by an even temperature-like parameter giving rise to a discontinuity of the ground-state energy density.

cond-mat.stat-mech↗

arXiv2014

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

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.

cond-mat.stat-mech↗

arXiv2014

The XYZ chain with Dzyaloshinsky-Moriya interactions: from spin-orbit-coupled lattice bosons to interacting Kitaev chains

Using the density-matrix renormalization-group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger-liquid behavior. Transitions from ferromagnetic to Luttinger-liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term turns out to split this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly-interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions.

cond-mat.stat-mech↗

arXiv2014

Finite-size scaling at first-order quantum transitions

We study finite-size effects at first-order quantum transitions (FOQTs). We show that the low-energy properties show a finite-size scaling (FSS) behavior, the relevant scaling variable being the ratio of the energy associated with the perturbation driving the transition and the finite-size energy gap at the FOQT point. The size dependence of the scaling variable is therefore essentially determined by the size dependence of the gap at the transition, which in turn depends on the boundary conditions. Our results have broad validity and, in particular, apply to any FOQT characterized by the degeneracy and crossing of the two lowest-energy states in the infinite-volume limit. In this case, a phenomenological two-level theory provides exact expressions for the scaling functions. Numerical results for the quantum Ising chain in transverse and parallel magnetic fields support the FSS ansatzes.

cond-mat.stat-mech↗

arXiv2014

Universal scaling effects of a temperature gradient at first-order transitions

We study the effects of smooth inhomogeneities at first-order transitions. We show that a temperature gradient at a thermally-driven first-order transition gives rise to nontrivial universal scaling behaviors with respect to the length scale of the variation of the local temperature T(x). We propose a scaling ansatz to describe the crossover region at the surface where T(x)=Tc, where the typical discontinuities of a first-order transition are smoothed out. The predictions of this scaling theory are checked, and get strongly supported, by numerical results for the 2D Potts models, for a sufficiently large number of q-states to have first-order transitions. Comparing with analogous results at the 2D Ising transition, we note that the scaling behaviors induced by a smooth inhomogeneity appear quite similar in first-order and continuous transitions.

cond-mat.stat-mech↗

arXiv2014

Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit

We investigate the ground-state properties of trapped fermion systems described by the Hubbard model with an external confining potential. We discuss the universal behaviors of systems in different regimes: from few particles, i.e. in dilute regime, to the trap thermodynamic limit. The asymptotic trap-size (TS) dependence in the dilute regime (increasing the trap size l keeping the particle number N fixed) is described by a universal TS scaling controlled by the dilute fixed point associated with the metal-to-vacuum quantum transition. This scaling behavior is numerically checked by DMRG simulations of the one-dimensional (1D) Hubbard model. In particular, the particle density and its correlations show crossovers among different regimes: for strongly repulsive interactions they approach those of a spinless Fermi gas, for weak interactions those of a free Fermi gas, and for strongly attractive interactions they match those of a gas of hard-core bosonic molecules. The large-N behavior of systems at fixed N/l corresponds to a 1D trap thermodynamic limit. We address issues related to the accuracy of the local density approximation (LDA). We show that the particle density approaches its LDA in the large-l limit. When the trapped system is in the metallic phase, corrections at finite l are O(l^{-1}) and oscillating around the center of the trap. They become significantly larger at the boundary of the fermion cloud, where they get suppressed as O(l^{-1/3}) only. This anomalous behavior arises from the nontrivial scaling at the metal-to-vacuum transition occurring at the boundaries of the fermion cloud.

cond-mat.quant-gas↗