Showing papers by "Ettore Vicari published in 2020"

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

Abstract: We consider a dynamic protocol for quantum many-body systems, which enables us 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. The competition of the two drivings is analyzed at quantum transitions, where the presence of critical correlations substantially changes the impact of local measurements. We identify a particular regime (dynamic scaling limit) within a dynamic scaling framework, where the two mechanisms develop a nontrivial interplay and peculiar scaling behaviors. This is supported by a numerical analysis of a measurement-driven quantum Ising chain. 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.

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

Abstract: This paper shows how open quantum systems subject to a slow passage across a Kibble-Zurek protocol can develop a universal dynamic scaling regime similar to that emerging in closed systems. The authors show that a fine tuning of the system-bath coupling is required and its decay rate should scale as a specific power of the time scale of the protocol, with the exponent being controlled by the universality class of the quantum transition.

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

Abstract: 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 $\mathrm{O}(M)$-symmetric multicomponent scalar models, whose symmetry is partially gauged to obtain $\mathrm{SU}({N}_{c})$ gauge theories, with a residual nonabelian global symmetry given by $U({N}_{f})$ for ${N}_{c}\ensuremath{\ge}3$ and $\mathrm{Sp}({N}_{f})$ for ${N}_{c}=2$, so that $M=2{N}_{c}{N}_{f}$. For ${N}_{f}=2$ and for all values of ${N}_{c}$ we investigated, ${N}_{c}=2$, 3, 4, these systems undergo a continuous finite-temperature transition, which belongs to a universality class related to the global symmetry group of the model. For ${N}_{c}=2$, since $\mathrm{Sp}(2)/{\mathbb{Z}}_{2}=\mathrm{SO}(5)$, it belongs to the O(5) vector universality class. For ${N}_{c}\ensuremath{\ge}3$, since $\mathrm{SU}(2)/{\mathbb{Z}}_{2}=\mathrm{SO}(3)$, it belongs to the O(3) vector universality class. For ${N}_{f}\ensuremath{\ge}3$, the numerical results show evidence of first-order transitions for any ${N}_{c}$. These results are in agreement with the predictions obtained by using the effective Landau-Ginzburg-Wilson approach in terms of a gauge-invariant order parameter. Our results indicate that the non-Abelian 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.

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

Abstract: 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 $\mathrm{SU}(N$) 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 $N\ensuremath{\ge}2$ 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 $\mathrm{SU}(N$) 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 $\mathrm{SU}(N$) 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 $N=25$.

Large-N behavior of three-dimensional lattice CP N−1 models

Abstract: We consider a three-dimensional lattice CP N−1 model, which corresponds to the lattice Abelian–Higgs model in the infinite gauge-coupling limit. We investigate its phase diagram and critical behavior in the large-N limit. We obtain numerical evidence that the model undergoes a first-order transition for sufficiently large values of N, i.e. for any 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 . 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.

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

Abstract: 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 monopole-free CP^{N-1} models.

Abstract: 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.

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

Abstract: We investigate the phase diagram and finite-temperature transitions of three-dimensional scalar $\mathrm{SO}({N}_{c})$ gauge theories with ${N}_{f}\ensuremath{\ge}2$ 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 $\mathrm{SO}({N}_{c})$ gauge theory, with O(${N}_{f}$) or $\mathrm{U}({N}_{f})$ global symmetry for ${N}_{c}\ensuremath{\ge}3$ 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 $\mathrm{SO}({N}_{c})$ gauge theory. The LGW approach predicts that the transition is of first order for ${N}_{f}\ensuremath{\ge}3$. 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 ${N}_{c}\ensuremath{\ge}3$. We perform numerical simulations for ${N}_{c}=3$ and ${N}_{f}=2,3$. The numerical results are in agreement with the LGW predictions.

Dynamics after quenches in one-dimensional quantum Ising-like systems

Abstract: We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter $g$ driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of $g$ around the critical value ${g}_{c}$, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of $g$. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest-neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular, the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.

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

Abstract: We address the interplay between global and local gauge non-Abelian symmetries in lattice gauge theories with multicomponent scalar fields. We consider two-dimensional lattice scalar non-Abelian gauge theories with a local $\mathrm{SO}({N}_{c})$ (${N}_{c}\ensuremath{\ge}3$) and a global $\mathrm{O}({N}_{f})$ invariance, obtained by partially gauging a maximally $\mathrm{O}({N}_{f}{N}_{c})$-symmetric multicomponent scalar model. Correspondingly, the scalar fields belong to the coset ${S}^{{N}_{f}{N}_{c}\ensuremath{-}1}/\mathrm{SO}({N}_{c})$, where ${S}^{N}$ is the $N$-dimensional sphere. In agreement with the Mermin-Wagner theorem, these lattice $\mathrm{SO}({N}_{c})$ gauge models with ${N}_{f}\ensuremath{\ge}3$ do not have finite-temperature transitions related to the breaking of the global non-Abelian $\mathrm{O}({N}_{f})$ 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 $\mathrm{O}(N)$ $\ensuremath{\sigma}$ 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 ${\mathrm{RP}}^{{N}_{f}\ensuremath{-}1}$ model.

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

Abstract: 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.

Two-dimensional multicomponent Abelian-Higgs lattice models

Abstract: 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 $\mathrm{SU}(N)$ symmetry. In agreement with the Mermin-Wagner theorem, the model has only a disordered phase at finite temperature, and a critical behavior is observed only 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 $C{P}^{N\ensuremath{-}1}$ field theory.

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

Abstract: 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 $u\sim t_s^{-\kappa}$ with increasing the time scale $t_s$ of the KZ protocol, where the exponent $\kappa = z/(y_\mu+z)$ depends on the dynamic exponent $z$ and the renormalization-group dimension $y_\mu$ 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.

Asymptotic low-temperature behavior of two-dimensional RP N − 1 models

Abstract: We investigate the low-temperature behavior of two-dimensional (2D) ${\mathrm{RP}}^{N\ensuremath{-}1}$ models, characterized by a global $\mathrm{O}(N)$ 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 $\mathrm{O}(3)\text{\ensuremath{-}}{\mathrm{RP}}^{2}$ 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) $\ensuremath{\sigma}$ model, suggesting the existence of a distinct 2D ${\mathrm{RP}}^{2}$ universality class. We also performed simulations for $N=4$, and the corresponding FSS results also support the existence of an ${\mathrm{RP}}^{3}$ universality class, different from the O(4) one.

Dissipative dynamics at first-order quantum transitions

Abstract: 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 $\mathrm{\ensuremath{\Delta}}$ of the lowest levels of the Hamiltonian, i.e., $u\ensuremath{\sim}\mathrm{\ensuremath{\Delta}}$. However, unlike continuous quantum transitions where $\mathrm{\ensuremath{\Delta}}$ is power-law suppressed, at first-order quantum transitions $\mathrm{\ensuremath{\Delta}}$ is exponentially suppressed with increasing the system size (provided the boundary conditions do not favor any particular phase).