arXiv subjects

Ettore Vicari

Publications and source records attributed to Ettore Vicari.

At least 73 records · Page 4Linked to original sources

arXiv2021

Two-dimensional lattice SU($N_c$) gauge theories with multiflavor adjoint scalar fields

We consider two-dimensional lattice SU($N_c$) gauge theories with $N_f$ real scalar fields transforming in the adjoint representation of the gauge group and with a global O($N_f$) invariance. Focusing on systems with $N_f\ge 3$, we study their zero-temperature limit, to understand under which conditions a continuum limit exists, and to investigate the nature of the associated quantum field theory. Extending previous analyses, we address the role that the gauge-group representation and the quartic scalar potential play in determining the nature of the continuum limit (when it exists). Our results further corroborate the conjecture that the continuum limit of two-dimensional lattice gauge models with multiflavor scalar fields, when it exists, is associated with a $σ$ model defined on a symmetric space that has the same global symmetry as the lattice model.

hep-lat↗

arXiv2021

Berezinskii-Kosterlitz-Thouless transitions in two-dimensional lattice SO($N_c$) gauge theories with two scalar flavors

We study the phase diagram and critical behavior of a two-dimensional lattice SO($N_c$) gauge theory ($N_c \ge 3$) with two scalar flavors, obtained by partially gauging a maximally O($2N_c$) symmetric scalar model. The model is invariant under local SO($N_c$) and global O(2) transformations. We show that, for any $N_c \ge 3$, it undergoes finite-temperature Berezinskii-Kosterlitz-Thouless (BKT) transitions, associated with the global Abelian O(2) symmetry. The transition separates a high-temperature disordered phase from a low-temperature spin-wave phase where correlations decay algebraically (quasi-long range order). The critical properties at the finite-temperature BKT transition and in the low-temperature spin-wave phase are determined by means of a finite-size scaling analysis of Monte Carlo data.

hep-lat↗

arXiv2020

Three-dimensional phase transitions in multiflavor lattice scalar SO(Nc) gauge theories

We investigate the phase diagram and finite-temperature transitions of three-dimensional scalar SO(Nc) gauge theories with Nf scalar flavors. These models are constructed starting from a maximally O(N)-symmetric multicomponent scalar model (N = Nc Nf), whose symmetry is partially gauged to obtain an SO(Nc) gauge theory, with O(Nf) or U(Nf) global symmetry for Nc > 2 or Nc = 2, respectively. These systems undergo finite-temperature transitions, where the global symmetry is broken. Their nature is discussed using the Landau-Ginzburg-Wilson (LGW) approach, based on a gauge-invariant order parameter, and the continuum scalar SO(Nc) gauge theory. The LGW approach predicts that the transition is of first order for Nf > 2. For Nf = 2 the transition is predicted to be continuous: it belongs to the O(3) vector universality class for Nc=2 and to the XY universality class for any Nc > 2. We perform numerical simulations for Nc = 3 and Nf = 2,3. The numerical results are in agreement with the LGW predictions.

cond-mat.stat-mech↗

arXiv2020

Dissipative dynamics at first-order quantum transitions

We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising model. We analyze the out-of-equilibrium dynamics arising from quenches of the Hamiltonian parameters and dissipative mechanisms modeled by a Lindblad master equation, with either local or global spin operators acting as dissipative operators. Analogously to what happens at continuous quantum transitions, we observe a regime where the system develops a nontrivial dynamic scaling behavior, which is realized when the dissipation parameter $u$ (globally controlling the decay rate of the dissipation within the Lindblad framework) scales as the energy difference $Δ$ of the lowest levels of the Hamiltonian, i.e., $u\sim Δ$. However, unlike continuous quantum transitions where $Δ$ is power-law suppressed, at first-order quantum transitions $Δ$ is exponentially suppressed with increasing the system size (provided the boundary conditions do not favor any particular phase).

cond-mat.stat-mech↗

arXiv2020

Higher-charge three-dimensional compact lattice Abelian-Higgs models

We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N>1 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gauge-invariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement/deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly-charged unit-length scalar fields with small and large number of components, i.e. N=2 and N=25.

cond-mat.stat-mech↗

arXiv2020

Lattice Abelian-Higgs model with noncompact gauge fields

We consider a noncompact lattice formulation of the three-dimensional electrodynamics with $N$-component complex scalar fields, i.e., the lattice Abelian-Higgs model with noncompact gauge fields. For any $N\ge 2$, the phase diagram shows three phases differing for the behavior of the scalar-field and gauge-field correlations: the Coulomb phase (short-ranged scalar and long-ranged gauge correlations), the Higgs phase (condensed scalar-field and gapped gauge correlations), and the molecular phase (condensed scalar-field and long-ranged gauge correlations). They are separated by three transition lines meeting at a multicritical point. Their nature depends on the coexisting phases and on the number $N$ of components of the scalar field. In particular, the Coulomb-to-molecular transition line (where gauge correlations are irrelevant) is associated with the Landau-Ginzburg-Wilson $Φ^4$ theory sharing the same SU($N$) global symmetry but without explicit gauge fields. On the other hand, the Coulomb-to-Higgs transition line (where gauge correlations are relevant) turns out to be described by the continuum Abelian-Higgs field theory with explicit gauge fields. Our numerical study is based on finite-size scaling analyses of Monte Carlo simulations with $C^*$ boundary conditions (appropriate for lattice systems with noncompact gauge variables, unlike periodic boundary conditions), for several values of $N$, i.e., $N=2, 4, 10, 15$, and $25$. The numerical results agree with the renormalization-group predictions of the continuum field theories. In particular, the Coulomb-to-Higgs transitions are continuous for $N\gtrsim 10$, in agreement with the predictions of the Abelian-Higgs field theory.

cond-mat.stat-mech↗

arXiv2020

Asymptotic low-temperature behavior of two-dimensional RP$^{N-1}$ models

We investigate the low-temperature behavior of two-dimensional (2D) RP$^{N-1}$ models, characterized by a global O($N$) symmetry and a local ${\mathbb Z}_2$ symmetry. For $N=3$ we perform large-scale simulations of four different 2D lattice models: two standard lattice models and two different constrained models. We also consider a constrained mixed O(3)-RP$^2$ model for values of the parameters such that vector correlations are always disordered. We find that all these models show the same finite-size scaling (FSS) behavior, and therefore belong to the same universality class. However, these FSS curves differ from those computed in the 2D O(3) $σ$ model, suggesting the existence of a distinct 2D RP$^2$ universality class. We also performed simulations for $N=4$, and the corresponding FSS results also support the existence of an RP$^3$ universality class, different from the O(4) one.

cond-mat.stat-mech↗

arXiv2020

Asymptotic low-temperature critical behavior of two-dimensional multiflavor lattice SO(Nc) gauge theories

We address the interplay between global and local gauge nonabelian symmetries in lattice gauge theories with multicomponent scalar fields. We consider two-dimensional lattice scalar nonabelian gauge theories with a local SO(Nc) (Nc >= 3) and a global O(Nf) invariance, obtained by partially gauging a maximally O(Nf x Nc)-symmetric multicomponent scalar model. Correspondingly, the scalar fields belong to the coset S(Nf Nc-1)/SO(Nc), where S(N) is the N-dimensional sphere. In agreement with the Mermin-Wagner theorem, these lattice SO(Nc) gauge models with Nf >= 3 do not have finite-temperature transitions related to the breaking of the global nonabelian O(Nf) symmetry. However, in the zero-temperature limit they show a critical behavior characterized by a correlation length that increases exponentially with the inverse temperature, similarly to nonlinear O(N) sigma models. Their universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the two-dimensional RP(Nf-1) model.

hep-lat↗

arXiv2020

Three-dimensional monopole-free CP(N-1) models

We investigate the phase diagram, and the nature of the phase transitions, of three-dimensional monopole-free CP(N-1) models, characterized by a global U(N) symmetry and a U(1) gauge symmetry, and the absence of monopoles. We present numerical analyses based on Monte Carlo simulations for N=2,4,10,15, and 25. We observe a finite-temperature transition in all cases, related to the condensation of a local gauge-invariant order parameter. For N=2 we are unable to draw any definite conclusion on the nature of the transition. The results may be interpreted by either a very weak first-order transition or a continuous transition with anomalously large scaling corrections. However, the results allow us to exclude that the system develops the critical behavior of the O(3) vector universality class, as it occurs in the standard three-dimensional CP(1) model without monopole suppression. For N=4,10,15, the transition is of first order, and significantly weaker than that observed in the presence of monopoles. For N=25 the results are consistent with a conventional continuous transition. We compare our results with the existing literature and with the predictions of different field-theory approaches. Our results are consistent with the scenario in which the model undergoes continuous transitions for large values of N, in agreement with analytic large-N calculations.

cond-mat.stat-mech↗

arXiv2020

Scaling properties of the dynamics at first-order quantum transitions when boundary conditions favor one of the two phases

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 fixed boundary conditions, favoring one of the two phases separated by the FOQT: more precisely, boundary conditions that favor the same magnetized phase (EFBC) or opposite phases (OFBC) at the two ends of the chain. These issues are investigated within the paradigmatic one-dimensional quantum Ising model, in which FOQTs are driven by the longitudinal magnetic field h. 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 time scale 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.

cond-mat.stat-mech↗

arXiv2020

Dynamic Kibble-Zurek scaling framework for open dissipative many-body systems crossing quantum transitions

We study the quantum dynamics of many-body systems, in the presence of dissipation due to the interaction with the environment, under Kibble-Zurek (KZ) protocols in which one Hamiltonian parameter is slowly, and linearly in time, driven across the critical value of a zero-temperature quantum transition. In particular we address whether, and under which conditions, open quantum systems can develop a universal dynamic scaling regime similar to that emerging in closed systems. We focus on a class of dissipative mechanisms whose dynamics can be reliably described through a Lindblad master equation governing the time evolution of the system's density matrix. We argue that a dynamic scaling limit exists even in the presence of dissipation, whose main features are controlled by the universality class of the quantum transition. This requires a particular tuning of the dissipative interactions, whose decay rate $u$ should scale as $u\sim t_s^{-κ}$ with increasing the time scale $t_s$ of the KZ protocol, where the exponent $κ= z/(y_μ+z)$ depends on the dynamic exponent $z$ and the renormalization-group dimension $y_μ$ of the driving Hamiltonian parameter. Our dynamic scaling arguments are supported by numerical results for KZ protocols applied to a one-dimensional fermionic wire undergoing a quantum transition in the same universality class of the quantum Ising chain, in the presence of dissipative mechanisms which include local pumping, decay, and dephasing.

cond-mat.stat-mech↗

arXiv2020

Measurement-induced dynamics of many-body systems at quantum criticality

We consider a dynamic protocol for quantum many-body systems, which enables to study the interplay between unitary Hamiltonian driving and random local projective measurements. While the unitary dynamics tends to increase entanglement, local measurements tend to disentangle, thus favoring decoherence. Close to a quantum transition where the system develops critical correlations with diverging length scales, the competition of the two drivings is analyzed within a dynamic scaling framework, allowing us to identify a regime (dynamic scaling limit) where the two mechanisms develop a nontrivial interplay. We perform a numerical analysis of this protocol in a measurement-driven Ising chain, which supports the scaling laws we put forward. The local measurement process generally tends to suppress quantum correlations, even in the dynamic scaling limit. The power law of the decay of the quantum correlations turns out to be enhanced at the quantum transition.

cond-mat.stat-mech↗

arXiv2020

Universal low-temperature behavior of two-dimensional lattice scalar chromodynamics

We study the role that global and local nonabelian symmetries play in two-dimensional lattice gauge theories with multicomponent scalar fields. We start from a maximally O($M$)-symmetric multicomponent scalar model, Its symmetry is partially gauged to obtain an SU($N_c$) gauge theory (scalar chromodynamics) with global U$(N_f)$ (for $N_c\ge 3$) or Sp($N_f$) symmetry (for $N_c=2$), where $N_f>1$ is the number of flavors. Correspondingly, the fields belong to the coset $S^M$/SU($N_c$) where $S^M$ is the $M$-dimensional sphere and $M=2 N_f N_c$. In agreement with the Mermin-Wagner theorem, the system is always disordered at finite temperature and a critical behavior only develops in the zero-temperature limit. Its universal features are investigated by numerical finite-size scaling methods. The results show that the asymptotic low-temperature behavior belongs to the universality class of the 2D CP$^{N_f-1}$ field theory for $N_c>2$, and to that of the 2D Sp($N_f$) field theory for $N_c=2$. These universality classes correspond to 2D statistical field theories associated with symmetric spaces that are invariant under Sp($N_f$) transformations for $N_c=2$ and under SU($N_f$) for $N_c > 2$. These symmetry groups are the same invariance groups of scalar chromodynamics, apart from a U(1) flavor symmetry that is present for $N_f \ge N_c > 2$, which does not play any role in determining the asymptotic behavior of the model.

hep-lat↗

arXiv2020

Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries

We study the nature of the finite-temperature transition of the three-dimensional scalar chromodynamics with N_f flavors. These models are constructed by considering maximally O(M)-symmetric multicomponent scalar models, whose symmetry is partially gauged to obtain SU(N_c) gauge theories, with a residual nonabelian global symmetry given by U(N_f) for N_c>2 and Sp(N_f) for N_c=2, so that M = 2 N_c N_f. We find that their finite-temperature transition is continuous for N_f=2 and for all values of Nc we investigated, N_c=2,3,4. Such continuous transitions belong to universality classes related to the global symmetry group of the theory. For N_c=2 it belongs to the SO(5)=Sp(2)/Z_2 universality class, while for N_c>2 it belongs to the SO(3)=SU(2)/Z_2 universality class. For N_f>2, the transition is always of first order. These results match the predictions obtained by using the effective Landau-Ginzburg-Wilson approach in terms of a gauge-invariant order parameter. Our results indicate that the nonabelian gauge degrees of freedom are irrelevant at the transition. These conclusions are supported by an analysis of gauge-field dependent correlation functions, that are always short-ranged, even at the transition.

cond-mat.stat-mech↗

arXiv2019

Large-N behavior of three-dimensional lattice CP(N-1) models

We investigate the phase diagram and critical behavior of a three-dimensional lattice CP(N-1) model in the large-N limit. Numerical evidence of first-order transitions is always observed for sufficiently large values of N, i.e. N>2 up to N=100. The transition becomes stronger---both the latent heat and the surface tension increase---as N increases. Moreover, on the high-temperature side, gauge fields decorrelate on distances of the order of one lattice spacing for all values of N considered. Our results are consistent with a simple scenario, in which the transition is of first order for any N, including N=\infty. We critically discuss the analytic large-N calculations that predicted a large-N continuous transition, showing that one crucial assumption made in these computations fails for the model we consider.

cond-mat.stat-mech↗

arXiv2019

Two-dimensional multicomponent Abelian-Higgs lattice models

We study the two-dimensional lattice multicomponent Abelian-Higgs model, which is a lattice compact U(1) gauge theory coupled with an N-component complex scalar field, characterized by a global SU(N) symmetry. In agreement with the Mermin-Wagner theorem, the model has only a disordered phase at finite temperature and a critical behavior is only observed in the zero-temperature limit. The universal features are investigated by numerical analyses of the finite-size scaling behavior in the zero-temperature limit. The results show that the renormalization-group flow of the 2D lattice N-component Abelian-Higgs model is asymptotically controlled by the infinite gauge-coupling fixed point, associated with the universality class of the 2D CP(N-1) field theory.

cond-mat.stat-mech↗

arXiv2019

Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions

We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the system with a Markovian bath, such that the evolution of the system's density matrix can be effectively described by a Lindblad master equation. We devise general scaling behaviors for the out-of-equilibrium evolution and the stationary states emerging in the large-time limit for generic initial conditions, in terms of the parameters of the Hamiltonian providing the coherent driving and those associated with the dissipative interactions with the environment. Our framework is supported by numerical results for the dynamics of a one-dimensional lattice fermion gas undergoing a quantum Ising transition, in the presence of dissipative mechanisms which include local pumping and decay of particles.

cond-mat.stat-mech↗

arXiv2019

Competing coherent and dissipative dynamics close to quantum criticality

We investigate the competition of coherent and dissipative dynamics in many-body systems at continuous quantum transitions. We consider dissipative mechanisms that can be effectively described by Lindblad equations for the density matrix of the system. The interplay between the critical coherent dynamics and dissipation is addressed within a dynamic finite-size scaling framework, which allows us to identify the regime where they develop a nontrivial competition. We analyze protocols that start from critical many-body ground states and put forward general dynamic scaling behaviors involving the Hamiltonian parameters and the coupling associated with the dissipation. This scaling scenario is supported by a numerical study of the dynamic behavior of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms such as local pumping, decaying, and dephasing.

cond-mat.stat-mech↗