Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields.

We investigate the nature of the deconfinement transitions in three-dimensional lattice Abelian Higgs models, in which a complex scalar field of integer charge Q≥2 is minimally coupled with a compact U(1) gauge field. Their phase diagram presents two phases separated by a transition line where static charges q, with q

Coulomb-Higgs phase transition of three-dimensional lattice Abelian Higgs gauge models with noncompact gauge variables and gauge fixing.

We study the critical behavior of three-dimensional (3D) lattice Abelian Higgs (AH) gauge models with noncompact gauge variables and multicomponent complex scalar fields, along the transition line between the Coulomb and Higgs phases. Previous works that focused on gauge-invariant correlations provided evidence that, for a sufficiently large number of scalar components, these transitions are continuous and associated with the stable charged fixed point of the renormalization-group flow of the 3D AH field theory (scalar electrodynamics), in which charged scalar matter is minimally coupled with an electromagnetic field. Here we extend these studies by considering gauge-dependent correlations of the gauge and matter fields, in the presence of two different gauge fixings, the Lorenz and the axial gauge fixing. Our results for N=25 are definitely consistent with the predictions of the AH field theory and therefore provide additional evidence for the characterization of the 3D AH transitions along the Coulomb-Higgs line as charged transitions in the AH field-theory universality class. Moreover, our results give additional insights on the role of the gauge fixing at charged transitions. In particular, we show that scalar correlations are critical only if a hard Lorenz gauge fixing is imposed.

Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system.

We discuss the quantum dynamics of an isolated composite system consisting of weakly interacting many-body subsystems. We focus on one of the subsystems, S, and study the dependence of its quantum correlations and decoherence rate on the state of the weakly-coupled complementary part E, which represents the environment. As a theoretical laboratory, we consider a composite system made of two stacked quantum Ising chains, locally and homogeneously weakly coupled. One of the chains is identified with the subsystem S under scrutiny, and the other one with the environment E. We investigate the behavior of S at equilibrium, when the global system is in its ground state, and under out-of-equilibrium conditions, when the global system evolves unitarily after a quench of the coupling between S and E. When S develops quantum critical correlations in the weak-coupling regime, the associated scaling behavior crucially depends on the quantum state of E, whether it is characterized by short-range correlations (analogous to those characterizing disordered phases in closed systems), algebraically decaying correlations (typical of critical systems), or long-range correlations (typical of magnetized ordered phases). In particular, different scaling behaviors, depending on the state of E, are observed for the decoherence of the subsystem S, as demonstrated by the different power-law divergences of the decoherence susceptibility that quantifies the sensitivity of the coherence to the interaction with E.

Quantum many-body spin rings coupled to ancillary spins: The sunburst quantum Ising model.

We study the ground-state properties of a quantum sunburst model, composed of a quantum Ising spin ring in a transverse field, symmetrically coupled to a set of ancillary isolated qubits, to maintain a residual translation invariance and also a Z_{2} symmetry. The large-size limit is taken in two different ways: either by keeping the distance between any two neighboring ancillary qubits fixed or by fixing their number while increasing the ring size. Substantially different regimes emerge, depending on the various Hamiltonian parameters: For small energy scale δ of the ancillary subsystem and small ring-qubit interaction κ, we observe rapid and nonanalytic changes in proximity to the quantum transitions of the Ising ring, both first order and continuous, which can be carefully controlled by exploiting renormalization-group and finite-size scaling frameworks. Smoother behaviors are instead observed when keeping δ>0 fixed and in the Ising disordered phase. The effect of an increasing number n of ancillary spins turns out to scale proportionally to sqrt[n] for sufficiently large values of n.

Scalar gauge-Higgs models with discrete Abelian symmetry groups.

We investigate the phase diagram and the nature of the phase transitions of three-dimensional lattice gauge-Higgs models obtained by gauging the Z_{N} subgroup of the global Z_{q} invariance group of the Z_{q} clock model (N is a submultiple of q). The phase diagram is generally characterized by the presence of three different phases, separated by three distinct transition lines. We investigate the critical behavior along the two transition lines characterized by the ordering of the scalar field. Along the transition line separating the disordered-confined phase from the ordered-deconfined phase, standard arguments within the Landau-Ginzburg-Wilson framework predict that the behavior is the same as in a generic ferromagnetic model with Z_{p} global symmetry, p being the ratio q/N. Thus, continuous transitions belong to the Ising and to the O(2) universality class for p=2 and p≥4, respectively, while for p=3 only first-order transitions are possible. The results of Monte Carlo simulations confirm these predictions. There is also a second transition line, which separates two phases in which gauge fields are essentially ordered. Along this line we observe the same critical behavior as in the Z_{q} clock model, as it occurs in the absence of gauge fields.

Critical crossover phenomena driven by symmetry-breaking defects at quantum transitions.

We study the effects of symmetry-breaking defects at continuous quantum transitions (CQTs) of homogeneous systems, which may arise from localized external fields coupled to the order-parameter operator. The problem is addressed within renormalization-group (RG) and finite-size scaling frameworks. We consider the paradigmatic one-dimensional quantum Ising models at their CQT, in the presence of defects which break the global Z_{2} symmetry. We show that such defects can give rise to notable critical crossover regimes where the ground-state properties experience substantial and rapid changes, from symmetric conditions to characterization of these crossover phenomena driven by defects. In particular, this is demonstrated by analyzing the ground-state fidelity associated with small changes of the defect strength. Within the critical crossover regime, the fidelity susceptibility shows a power-law divergence when increasing the system size, related to the RG dimension of the defect strength; in contrast, outside the critical defect regime, it remains finite. We support the RG scaling arguments with numerical results.

Breaking of Gauge Symmetry in Lattice Gauge Theories.

We study perturbations that break gauge symmetries in lattice gauge theories. As a paradigmatic model, we consider the three-dimensional Abelian-Higgs (AH) model with an N-component scalar field and a noncompact gauge field, which is invariant under U(1) gauge and SU(N) transformations. We consider gauge-symmetry breaking perturbations that are quadratic in the gauge field, such as a photon mass term and determine their effect on the critical behavior of the gauge-invariant model, focusing mainly on the continuous transitions associated with the charged fixed point of the AH field theory. We discuss their relevance and compute the (gauge-dependent) exponents that parametrize the departure from the critical behavior (continuum limit) of the gauge-invariant model. We also address the critical behavior of lattice AH models with broken gauge symmetry, showing an effective enlargement of the global symmetry, from U(N) to O(2N), which reflects a peculiar cyclic renormalization-group flow in the space of the lattice AH parameters and of the photon mass.

Lattice gauge theories in the presence of a linear gauge-symmetry breaking.

We study the effects of gauge-symmetry breaking (GSB) perturbations in three-dimensional lattice gauge theories with scalar fields. We study this issue at transitions in which gauge correlations are not critical and the gauge symmetry only selects the gauge-invariant scalar degrees of freedom that become critical. A paradigmatic model in which this behavior is realized is the lattice CP^{1} model or, more generally, the lattice Abelian-Higgs model with two-component complex scalar fields and compact gauge fields. We consider this model in the presence of a linear GSB perturbation. The gauge symmetry turns out to be quite robust with respect to the GSB perturbation: the continuum limit is gauge invariant also in the presence of a finite small GSB term. We also determine the phase diagram of the model. It has one disordered phase and two phases that are tensor and vector ordered, respectively. They are separated by continuous transition lines, which belong to the O(3), O(4), and O(2) vector universality classes, and which meet at a multicritical point. We remark that the behavior at the CP^{1} gauge-symmetric critical point substantially differs from that at transitions in which gauge correlations become critical, for instance at transitions in the noncompact lattice Abelian-Higgs model that are controlled by the charged fixed point: in this case, the behavior is extremely sensitive to GSB perturbations.

Phase diagram and Higgs phases of three-dimensional lattice SU(N_{c}) gauge theories with multiparameter scalar potentials.

We consider three-dimensional lattice SU(N_{c}) gauge theories with degenerate multicomponent (N_{f}>1) complex scalar fields that transform under the fundamental representation of the gauge SU(N_{c}) group and of the global U(N_{f}) invariance group, interacting with the most general quartic potential compatible with the global (flavor) and gauge (color) symmetries. We investigate the phase diagrams, identifying the low-temperature Higgs phases and their global and gauge symmetries, and the critical behaviors along the different transition lines. In particular, we address the role of the quartic scalar potential, which determines the Higgs phases and the corresponding symmetry-breaking patterns. Our study is based on the analysis of the minimum-energy configurations and on numerical Monte Carlo simulations. Moreover, we investigate whether some of the transitions observed in the lattice model can be related to the behavior of the renormalization-group flow of the continuum field theory with the same symmetries and field content around its stable charged fixed points. For N_{c}=2, numerical results are consistent with the existence of charged critical behaviors for N_{f}>N_{f}^{★}, with 20

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 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.

Three-dimensional phase transitions in multiflavor lattice scalar SO(N_{c}) gauge theories.

We investigate the phase diagram and finite-temperature transitions of three-dimensional scalar SO(N_{c}) gauge theories with N_{f}≥2 scalar flavors. These models are constructed starting from a maximally O(N)-symmetric multicomponent scalar model (N=N_{c}N_{f}), whose symmetry is partially gauged to obtain an SO(N_{c}) gauge theory, with O(N_{f}) or U(N_{f}) global symmetry for N_{c}≥3 or N_{c}=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(N_{c}) gauge theory. The LGW approach predicts that the transition is of first order for N_{f}≥3. For N_{f}=2 the transition is predicted to be continuous: It belongs to the O(3) vector universality class for N_{c}=2 and to the XY universality class for any N_{c}≥3. We perform numerical simulations for N_{c}=3 and N_{f}=2,3. The numerical results are in agreement with the LGW predictions.

Three-dimensional monopole-free CP

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, 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 in terms of either a weak first-order transition or a continuous transition with anomalously large scaling corrections. However, the results allow us to exclude that the transition belongs to the O(3) vector universality class, as it occurs in the standard three-dimensional CP^{1} model without monopole suppression. For N=4,10,and15, 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. They are consistent with the scenario in which the model undergoes continuous transitions for large values of N, including N=∞, in agreement with analytic large-N calculations for the N-component Abelian-Higgs model.

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≥2 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 and 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.

Phase Diagram, Symmetry Breaking, and Critical Behavior of Three-Dimensional Lattice Multiflavor Scalar Chromodynamics.

We study the nature of the phase diagram of three-dimensional lattice models in the presence of non-Abelian gauge symmetries. In particular, we consider a paradigmatic model for the Higgs mechanism, lattice scalar chromodynamics with N_{f} flavors, characterized by a non-Abelian SU(N_{c}) gauge symmetry. For N_{f}≥2 (multiflavor case), it presents two phases separated by a transition line where a gauge-invariant order parameter condenses, being associated with the breaking of the residual global symmetry after gauging. The nature of the phase transition line is discussed within two field-theoretical approaches, the continuum scalar chromodynamics, and the Landau-Ginzburg-Wilson (LGW) Φ^{4} approach based on a gauge-invariant order parameter. Their predictions are compared with simulation results for N_{f}=2, 3 and N_{c}=2-4. The LGW approach turns out to provide the correct picture of the critical behavior at the transitions between the two phases.

Multicomponent compact Abelian-Higgs lattice models.

We investigate the phase diagram and critical behavior of three-dimensional multicomponent Abelian-Higgs models, in which an N-component complex field z_{x}^{a} of unit length and charge is coupled to compact quantum electrodynamics in the usual Wilson lattice formulation. We determine the phase diagram and study the nature of the transition line for N=2 and N=4. Two phases are identified, specified by the behavior of the gauge-invariant local composite operator Q_{x}^{ab}=z[over ¯]_{x}^{a}z_{x}^{b}-δ^{ab}/N, which plays the role of order parameter. In one phase, we have 〈Q_{x}^{ab}〉=0, while in the other Q_{x}^{ab} condenses. Gauge correlations are never critical: gauge excitations are massive for any finite coupling. The two phases are separated by a transition line. Our numerical data are consistent with the simple scenario in which the nature of the transition is independent of the gauge coupling. Therefore, for any finite positive value of the gauge coupling, we predict a continuous transition in the Heisenberg universality class for N=2 and a first-order transition for N=4. However, notable crossover phenomena emerge for large gauge couplings, when gauge fluctuations are suppressed. Such crossover phenomena are related to the unstable O(2N) fixed point, describing the behavior of the model in the infinite gauge-coupling limit.

Three-dimensional ferromagnetic CP

We investigate the critical behavior of three-dimensional ferromagnetic CP^{N-1} models, which are characterized by a global U(N) and a local U(1) symmetry. We perform numerical simulations of a lattice model for N=2, 3, and 4. For N=2 we find a critical transition in the Heisenberg O(3) universality class, while for N=3 and 4 the system undergoes a first-order transition. For N=3 the transition is very weak and a clear signature of its discontinuous nature is only observed for sizes L≳50. We also determine the critical behavior for a large class of lattice Hamiltonians in the large-N limit. The results confirm the existence of a stable large-NCP^{N-1} fixed point. However, this evidence contradicts the standard picture obtained in the Landau-Ginzburg-Wilson (LGW) framework using a gauge-invariant order parameter: The presence of a cubic term in the effective LGW field theory for any N≥3 would usually be taken as an indication that these models generically undergo first-order transitions.

Dynamic finite-size scaling after a quench at quantum transitions.

We present a general dynamic finite-size scaling theory for the quantum dynamics after an abrupt quench, at both continuous and first-order quantum transitions. For continuous transitions, the scaling laws are naturally ruled by the critical exponents and the renormalization-group dimension of the perturbation at the transition. In the case of first-order transitions, it is possible to recover a universal scaling behavior, which is controlled by the size behavior of the energy gap between the lowest-energy levels. We discuss these findings in the framework of the paradigmatic quantum Ising ring, and support the dynamic scaling laws by numerical evidence.

Criticality of O(N) symmetric models in the presence of discrete gauge symmetries.

We investigate the critical properties of the three-dimensional antiferromagnetic RP^{N-1} model, which is characterized by a global O(N) symmetry and a discrete Z_{2} gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group flow of the most general Φ^{4} theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For N=4 no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of O(N) symmetric models with a discrete Z_{2} gauge symmetry.

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, slowly driven across a thermal first-order transition, where the equilibrium dynamics is exponentially slow. We consider a dynamics that starts in the high-T phase at time t=t_{i}<0 and ends at t=t_{f}>0 in the low-T phase, with a time-dependent temperature T(t)/T_{c}≈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=20 and 10. 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.

Dynamic finite-size scaling at first-order transitions.

We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. This is characterized by an exponentially large time scale related to the tunneling between the two phases. We show that, when considering time scales of the order of the tunneling time, the dynamic behavior can be described by a two-state coarse-grained dynamics. This allows us to obtain exact predictions for the dynamical scaling functions. To test the general DFSS theory at FOTs, we consider the two-dimensional Ising model in the low-temperature phase, where the external magnetic field drives a FOT, and the 20-state Potts model, which undergoes a thermal FOT. Numerical results for a purely relaxational dynamics fully confirm the general theory.