Breaking Perturbations Research Articles

Finite-size generators for weak integrability breaking perturbations in the Heisenberg chain

Finite-size generators for weak integrability breaking perturbations in the Heisenberg chain

FLARE: field line analysis and reconstruction for 3D boundary plasma modeling

Abstract The FLARE code is a magnetic mesh generator that is integrated within a suite of tools for the analysis of the magnetic geometry in toroidal fusion devices. A magnetic mesh is constructed from field line segments and permits fast reconstruction of field lines in 3D boundary plasma codes such as EMC3-EIRENE. Both intrinsically non-axisymmetric configurations (stellarators) and those with symmetry breaking perturbations of an axisymmetric equilibrium (tokamaks) are supported. The code itself is written in Modern Fortran with MPI support for parallel computing, and it incorporates object-oriented programming for the definition of the magnetic field and the material surface geometry. Extended derived types for a number of different magnetohydrodynamic equilibrium and plasma response models are implemented. The core element of FLARE is a field line tracer with adaptive step-size control, and this is integrated into tools for the construction of Poincaré maps and invariant manifolds of X-points. A collection of high-level procedures that generate output files for visualization is build on top of that. The analysis modules are build with Python frontends that facilitate customization of tasks and/or scripting of parameter scans.

Iterative Construction of Conserved Quantities in Dissipative Nearly Integrable Systems.

Integrable systems offer rare examples of solvable many-body problems in the quantum world. Because of the fine-tuned structure, their realization in nature and experiment is never completely accurate, and therefore effects of integrability are observed only transiently. One way to overcome this limitation is to weakly couple nearly integrable systems to baths and driving: this will stabilize integrable effects up to arbitrary time and encode them in the stationary state approximated by a generalized Gibbs ensemble. However, the description of such driven dissipative nearly integrable models is challenging and no exact analytical methods have been proposed so far. Here, we develop an iterative scheme in which integrability breaking perturbations (baths) determine the conserved quantities that play the leading role in a highly efficient truncated generalized Gibbs ensemble description. Our scheme paves the way for easier calculations in thermodynamically large systems and can be used to construct unknown conserved quantities.

Charge Correlations in Cuprate Superconductors

High-temperature superconductivity, with transition temperatures up to ≈134 K at ambient pressure, occurs in layered cuprate compounds. The conducting CuO2 planes, which are universally present, are responsible for the superconductivity but also show a disposition to other competing states including spin and charge order. Charge-density-wave (CDW) order appears to be a universal property of cuprate superconductors. It has been studied via a multitude of probes including X-ray and neutron scattering, nuclear magnetic resonance, scanning probe techniques, electronic transport, and quantum oscillations. Here, we review the microscopic properties of the CDW order. We discuss the nature of the ordered state, that is, its symmetry and microscopic structure. Furthermore, we show how the CDW order is related to quenched disorder, host structure, symmetry breaking perturbations, and magnetic fields. We also describe measurements of dynamic collective charge excitations that are closely related to the quasi-static CDW order. Finally, we highlight some of the debated issues in the field, including the origin of the CDW order, the relationship to spin order, and the nature of the spatial CDW correlations.

Weak integrability breaking perturbations of integrable models

Weak integrability breaking perturbations of integrable models

Topological pump of SU(Q) quantum chain and Diophantine equation

A topological pump of the $SU(Q)$ quantum chain is proposed associated with a current due to a local $[U(1)]^{\otimes Q}$ gauge invariance of colored fermions. The $SU(Q)$ invariant dimer phases are characterized by the $Z_Q$ Berry phases as a topological order parameter with a $d$-dimensional twist space ($d=Q-1$) as a synthetic Brillouin zone. By inclusion of the symmetry breaking perturbation specified by a rational parameter $\Phi=P/Q$, the pump, that encloses around the phase boundary, is characterized by the $Q$ Chern numbers associated with the currents due to uniform infinitesimal twists. The analysis of the systems under the open/periodic/twisted boundary conditions clarifies the bulk-edge correspondence of the pump where the large gauge transformation generated by the center of mass (CoM) plays a central role. An explicit formula for the Chern number is given by using the Diophanine equation. Numerical demonstration by the exact diagonalization and the DMRG for finite systems ($Q=3,4$ and $5$) have been presented to confirm the general discussions for low energy spectra, edge states, CoM's, Chern numbers and the bulk-edge correspondence. A modified Lieb-Schultz-Mattis type argument for the general $SU(Q)$ quantum chain is also mentioned.

Phase transitions as a manifestation of spontaneous unitarity violation

Spontaneous symmetry breaking is well understood under equilibrium conditions as a consequence of the singularity of the thermodynamic limit. How a single global orientation of the order parameter dynamically emerges from an initially symmetric state during a phase transition, however, is not captured by this paradigm. Here, we present a series of symmetry arguments suggesting that singling out a global choice for the ordered state is in fact forbidden under unitary time evolution, even in the presence of an environment and infinitesimal symmetry breaking perturbations. We thus argue that the observation of phase transitions in our everyday world presents a manifestation of the unitarity of quantum dynamics itself being spontaneously broken. We argue that this agrees with the observation that Schrödinger’s time dependent equation is rendered unstable for macroscopic objects owing to the same singular thermodynamic limit that affects equilibrium configurations.

Z2 Dirac points with topologically protected multihelicoid surface states

In some Dirac systems with time-reversal ($\mathcal{T}$) and glide ($\mathcal{G}$) symmetries, multihelicoid surface states (MHSSs) appear, as discussed in various systems such as electronic and photonic ones. However, the topological nature and the conditions for the appearance of the MHSSs have not been understood. Here we show that MHSSs result from bulk-surface correspondence for the ${Z}_{2}$ monopole charge $\mathcal{Q}$, which cannot be defined as a local quantity associated with the Dirac point, unlike the $Z$ monopole charge characterizing Weyl points. The previously known formula of $\mathcal{Q}$ turns out to be non-gauge-invariant and thus cannot characterize the MHSSs. This shortcoming of the definition of $\mathcal{Q}$ is amended by redefining $\mathcal{Q}$ as a global topological invariant in $k$-space. Surprisingly, the newly defined $\mathcal{Q}$, characterizing $\mathcal{GT}$ invariant gapless systems, is equal to the $\mathcal{G}$-protected ${Z}_{2}$ topological invariant $\ensuremath{\nu}$, which is nontrivial only in $\mathcal{T}$-breaking gapped systems. This global definition of $\mathcal{Q}$ automatically guarantees the appearance of MHSSs even when the Dirac point splits into Weyl points or a nodal ring by lowering the symmetry, as long as the $\mathcal{GT}$ symmetry is preserved. $\mathcal{Q}$ can be simplified to symmetry-based indicators when two vertical $\mathcal{G}\mathrm{s}$ are preserved, and filling-enforced topological crystalline insulators are diagnosed in several cases when a $\mathcal{T}$-breaking perturbation is induced. Material candidate ${\mathrm{Li}}_{2}{\mathrm{B}}_{4}{\mathrm{O}}_{7}$ together with a list of space groups preserving MHSSs are also proposed.

Fermionic approach to variational quantum simulation of Kitaev spin models

We use the variational quantum eigensolver (VQE) to simulate Kitaev spin models with and without integrability breaking perturbations, focusing in particular on the honeycomb and square-octagon lattices. These models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation and is capable of expressing the exact ground state in the solvable limit. We also demonstrate that this ansatz can be extended beyond this limit to provide excellent accuracy when compared to other VQE approaches. In certain cases, this fermionic representation is advantageous because it reduces by a factor of two the number of qubits required to perform the simulation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.

Critical structure and emergent symmetry of Dirac fermion systems

Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross–Neveu–Yukawa (GNY) model. Using the first-order ε expansion in dimensions, we study the critical structure and emergent symmetry of the O(N)-GNY model with N f flavors of four-component Dirac fermions coupled strongly to an O(N) scalar field under a small O(N)-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general N and N f . Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for on the basis of O(N)-GNY model. It turns out that the O(N)-GNY universality class is physically meaningful if and only if . On this premise, the small O(N)-symmetry breaking perturbation is always irrelevant in the O(N)-GNY universality class. Our studies show that the emergent symmetry in Dirac systems has an upper limit , depending on the flavor numbers N f . As a result, the emergent-O(4) and O(5) symmetries are possible to be found in Dirac systems with fermion flavor , and the emergent-O(4), O(5), O(6) and O(7) symmetries are expected to be found in the systems with fermion flavor . Our result suggests some richer transitions with emergent- symmetry, and so on. Interestingly, in the O(4)-GNY universality class, we find that there is a new supersymmetric critical point which is expected to be found in Dirac systems with fermion flavor .

Bose-Hubbard realization of fracton defects

Bose-Hubbard models are simple paradigmatic lattice models used to study dynamics and phases of quantum bosonic matter. We combine the extended Bose-Hubbard model in the hard-core regime with ring-exchange hoppings. By investigating the symmetries and low-energy properties of the Hamiltonian we argue that the model hosts fractonic defect excitations. We back up our claims with exact numerical simulations of defect dynamics exhibiting mobility constraints. Moreover, we confirm the robustness of our results against fracton symmetry breaking perturbations. Finally we argue that this model can be experimentally realized in recently proposed quantum simulator platforms with big time crystals, thus paving a way for the controlled study of many-body dynamics with mobility constraints.

Dynamical crossover behavior in the relaxation of quenched quantum many-body systems

A crossover between different power-law relaxation behaviors of many-body periodically driven integrable systems has come to light in recent years. We demonstrate using integrable quantum systems, that similar kinds of dynamical transitions may also occur in the relaxation of such systems following a sudden quench. Particularly, we observe two distinct power-law relaxation behaviors following a sudden quench in the integrable XY model, depending upon whether the quenched Hamiltonian lies in the commensurate or the incommensurate phase. The relaxation behavior for quenches at and near the boundary line, called the disorder line (DL), separating these phases is also characterized. The relaxation at the DL shows a new scaling exponent previously unexplored. The transitions occur through a crossover from the commensurate/incommensurate scaling behavior to the DL scaling behavior. The crossover time diverges like a power law as the parameters of the final quenched Hamiltonian approach the DL. The transitions are also observed to be robust under weak integrability breaking perturbations but disappear following strongly chaotic quenches.

Pseudo-bounces vs. new instantons

Some false vacua do not decay via bounces. This usually happens when a flat direction of the tunneling action due to scale invariance is lifted to a sloping valley by a scale breaking perturbation, pushing the bounce off to infinity. We compare two types of alternative decay configurations that have been proposed recently to describe decay in such cases: pseudo-bounces and new instantons. Although both field configurations are quite similar, we find that the pseudo-bounce action is lower than the new instanton one and describes more faithfully the bottom of the action valley. In addition, pseudo-bounces cover a range of field space wider than new instantonsand, as a result, lead to a decay rate that can be lower than the one via new instantons by orders of magnitude.

Selection rules for breaking selection rules

Floquet systems often exhibit dynamical symmetries (DS) that govern the time-dependent dynamics and result in selection rules. When a DS is broken, selection rule deviations are expected. Typically, information about the symmetry-breaking perturbation/phase and the time-dependent dynamics can be extracted from these deviations, hence they are regarded as a background free gauge of symmetry breaking. However, to date, DS breaking & selection rule deviations are not described by a general approach, thus there is no universal insight about the interplay between selection rule deviations, the symmetry breaking perturbation, and the broken DS. Here we consider DS breaking in Floquet systems from a general standpoint, formulating a general theory that analytically connects the symmetry-broken and fully symmetric systems. Using an external laser (of arbitrary frequency and polarization), as a model DS breaking perturbation, we discover that the broken symmetry systematically imposes selection rules on the symmetry-broken system, which physically manifest as scaling laws of selection rule deviations. We term these rules ‘selection rules for breaking selection rules’—a new concept in physics. We numerically validate the analytical theory in the context of high harmonic generation. Our discovery is a general feature of nonlinear wave-mixing phenomena, and we expect it to apply to any Floquet system (classical & quantum) and to any DS breaking mechanism (either by intrinsic or extrinsic elements of the system).

Fourth-order exceptional points in correlated quantum many-body systems

Non-Hermtian (NH) Hamiltonians effectively describing the physics of dissipative systems have become an important tool with applications ranging from classical meta-materials to quantum many-body systems. Exceptional points, the NH counterpart of spectral degeneracies, are among the paramount phenomena unique to the NH realm. While realizations of second-order exceptional points have been reported in a variety of microscopic models, higher-order ones have largely remained elusive in the many-body context, as they in general require fine tuning in high-dimensional parameter spaces. Here, we propose a microscopic model of correlated fermions in three spatial dimensions and demonstrate the occurrence of interaction-induced fourth-order exceptional points that are protected by chiral symmetry. We demonstrate their stability against symmetry breaking perturbations and investigate their characteristic analytical and topological properties.

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.

Polarization conversion in anisotropic dielectric metasurfaces originating from bound states in the continuum.

We use the semianalytical Cartesian multipole method to investigate the light transmission and reflection spectra of anisotropic dielectric metasurfaces, and extend the multipole decompositions method to account for cross-polarization conversion effects. We observe sharp high-Q resonances arising from a distortion of symmetry-protected bound states in the continuum in asymmetric dielectric metasurfaces, i.e., quasibound states in the continuum. In addition, by further introducing in-plane symmetric breaking perturbation, the polarization conversions of linearly polarized light can be achieved through quasibound states in the continuum. With the aid of temporal coupled-mode theory, we can obtain the limit of cross-conversion under single high-Q resonance, i.e., 0.25. Our work will help to design dielectric metasurfaces to control the polarization states of light.

Transport and spectral properties of magic-angle twisted bilayer graphene junctions based on local orbital models

The electronic properties of junctions defined electrostatically on twisted bilayer graphene can be addressed theoretically using lattice models. Recent works have introduced minimal local orbital models to describe twisted bilayer graphene at the magic angle (MATBLG) with different degrees of approximation and accounting for fragile topology. In the present work we use a Green's function formalism to obtain the spectral and transport properties for MATBLG junctions based on these models. We introduce different symmetry breaking perturbations to simulate the effect of interactions and characterize the topology of the bulk bands by analyzing the corresponding Wilson loops. We then analyze the spectral properties for different types of edges and in the case of a domain wall in the sublattice symmetry breaking parameter. We further consider a three region junction where one could control independently the central and lateral regions doping level. In the limit where the central region is fixed at the charge neutrality point and the lateral ones are heavily doped, the spectral and the two terminal transport properties can be understood in terms of the hybridization of chiral states along the junctions. These properties are found to be extremely sensitive to the orientation of the junctions along the moir\'e lattice.

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.

Long-lived nonthermal states in pumped one-dimensional systems of hard-core bosons

We study a unitary time evolution of a symmetry-broken state in a form of a charge density wave in a finite system of interacting hard-core bosons, which can be mapped onto the XXZ Heisenberg chain. Moreover, we introduce a spatially-homogenous and time-dependent vector potential that mimics a short laser pulse. We establish the range of amplitudes of the vector potential for which the onset of charge density wave order can be controlled. We propose a protocol that reveals non-thermal long-lived states, which are characterized by a non-zero charge density wave order translated by one lattice site with respect to its initial formation. The life times of these states are large in comparison to all typical times given by the parameters of the system. They increase with the number of lattice sites, but are significantly suppressed by the integrablility breaking perturbations. In view of these findings, we speculate that the long-lived non-thermal states exist in the thermodynamic limit.