Spontaneous Breaking Of Continuous Symmetry Research Articles

Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

The Mermin-Wagner theorem states that spontaneous continuous symmetry breaking is prohibited in systems with short-range interactions at spatial dimension D ≤ 2. For long-range interactions with a power-law form (1/rα), the theorem further forbids ferromagnetic or antiferromagnetic order at finite temperature when α ≥ 2D. However, the situation for α ∈ (2, 4) at D = 2 is not covered by the theorem. To address this, we conduct large-scale quantum Monte Carlo simulations and field theoretical analysis. Our findings show spontaneous breaking of SU(2) symmetry in the ferromagnetic Heisenberg model with 1/rα-form long-range interactions at D = 2. We determine critical exponents through finite-size analysis for α < 3 (above the upper critical dimension with Gaussian fixed point) and 3 ≤ α < 4 (below the upper critical dimension with non-Gaussian fixed point). These results reveal new critical behaviors in 2D long-range Heisenberg models, encouraging further experimental studies of quantum materials with long-range interactions beyond the Mermin-Wagner theorem’s scope.

Bright solitons in spontaneously formed polariton networks

Bright solitons in a polariton fluid are excitations with a comparatively high intensity that flow without dissipation in spite of a finite lifetime of polaritons. Under resonant driving conditions, bright polariton solitons can be created using a two-beam excitation scheme which includes a plane-wave pump and a focused beam injecting a soliton at a certain location [O. A. Egorov et al., PRL 102, 153904 (2009)]. Here we discuss a new mechanism of soliton formation which takes place under plane-wave driving in a perfectly uniform microcavity wire—i.e., with no writing beams or seeding inhomogeneities. The key phenomenon underlying formation of solitons in this case is the spontaneous breaking of continuous symmetry and onset of periodic spin networks [S. S. Gavrilov, PRL 120, 033901 (2018)].

Are there Goldstone bosons in d≤z+1 ?

We study the viability of spontaneous breaking of continuous symmetries in theories with Lifshitz scaling, according to the number of space-time dimensions $d$ and the dynamical scaling $z$. Then, the answer to the question in the title is no (quantum field theoretically) and yes (holographically). With field theory tools, we show that symmetry breaking is indeed prevented by large quantum fluctuations when $d\leq z+1$, as expected from scaling arguments. With holographic tools, on the other hand, we find nothing that prevents the existence of a vacuum expectation value. This difference is made possible by the large $N$ limit of holography. An important subtlety in this last framework is that in order to get a proper description of a conserved current, renormalization of the temporal mode of the bulk vector requires an alternative quantization. We also comment on the implications of turning on temperature.

Collective Modes in Excitonic Magnets: Dynamical Mean-Field Study.

We present a dynamical mean-field study of dynamical susceptibilities in the two-band Hubbard model. Varying the model parameters we analyze the two-particle excitations in the normal as well as in the ordered phase, an excitonic condensate. The two-particle dynamical mean-field theory spectra in the ordered phase reveal the gapless Goldstone modes arising from spontaneous breaking of continuous symmetries. We also observe the gapped Higgs mode, characterized by vanishing of the gap at the phase boundary. Qualitative changes observed in the spin susceptibility can be used as an experimental probe to identify the excitonic condensation.

Excitation of Higgs Mode in Superfluid Fermi Gas in BCS–BEC Crossover

In quantum many-body systems with spontaneous breaking of continuous symmetries, Higgs modes emerge as collective amplitude oscillations of order parameters. Recently, Higgs mode has been observed in the ultracold Fermi gas. In the present paper, we use the time-dependent Bogoliubov-de Gennes equations to investigate Higgs amplitude oscillations of the superfluid order parameter in a Fermi gas induced by a rapid change of the ${\it s}$-wave scattering length. In particular, we investigate the Higgs mode with different values of the initial scattering length. We find that the energy of the Higgs mode coincides with the threshold energy of the pair-breaking excitation, and exponent of the power-low decay of the Higgs mode $\gamma$ continuously changes between $\gamma=-1/2$ and $\gamma=-3/2$ through the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. Moreover, we propose the optimal ramp speed of the scattering length for observing the clearest Higgs oscillations.

Thouless-Valatin rotational moment of inertia from linear response theory

Spontaneous breaking of continuous symmetries of a nuclear many-body system results in appearance of zero-energy restoration modes. Such modes introduce a non-physical contributions to the physical excitations called spurious Nambu-Goldstone modes. Since they represent a special case of collective motion, they are sources of important information about the Thouless-Valatin inertia. The main purpose of this work is to study the Thouless-Valatin rotational moment of inertia as extracted from the Nambu-Goldstone restoration mode that results from the zero-frequency response to the total angular momentum operator. We examine the role and effects of the pairing correlations on the rotational characteristics of heavy deformed nuclei in order to extend our understanding of superfluidity in general. We use the finite amplitude method of the quasiparticle random phase approximation on top of the Skyrme energy density functional framework with the Hartree-Fock-Bogoliubov theory. We have successfully extended this formalism and established a practical method for extracting the Thouless-Valatin rotational moment of inertia from the strength function calculated in the symmetry restoration regime. Our results reveal the relation between the pairing correlations and the moment of inertia of axially deformed nuclei of rare-earth and actinide regions of the nuclear chart. We have also demonstrated the feasibility of the method for obtaining the moment of inertia for collective Hamiltonian models. We conclude that from the numerical and theoretical perspective, the finite amplitude method can be widely used to effectively study rotational properties of deformed nuclei within modern density functional approaches.

Projected Symmetry Breaking in Dipole-Locked $$^3$$ 3 He-B

We show theoretically that a collision of two superfluid droplets can effectively cause a two-dimensional symmetry breaking phase transition. Three-dimensional nucleation of quantized vortices and/or hedgehogs in the collision are considered the formation of domain walls and/or point vortices due to the Kibble–Zurek mechanism in a projected two-dimensional space. This problem is generally applicable to arbitrarily ordered media that undergo spontaneous breaking of continuous symmetries.

Coherence of two-dimensional electron-hole systems: Spontaneous breaking of continuous symmetries: A review

The spontaneous breaking of the continuous symmetries of a two-dimensional electron-hole system in a strong magnetic field perpendicular to the plane leads to the formation of new ground states and determines the energy spectrum of collective elementary excitations that appear above these new ground states. In this review, the main attention is paid to the electron-hole system formed from coplanar magnetoexcitons under conditions of Bose-Einstein condensation in the ground state with the wave vector k = 0 taking into account the influence of excited Landau levels, when exciton-type elementary excitations coexist with plasmon-type oscillations. At the same time, the properties of a two-component system consisting of a two-dimensional electron gas and a two-dimensional hole gas spatially separated in a double quantum well under conditions of the fractional quantum Hall effect are of great interest, because these properties can affect the quantum states of magnetic excitons that are formed when the distance between the layers tends to zero. Bilayer electron systems are also considered under conditions of the fractional quantum Hall effect with the one-half filling factor for each layer and the total filling factor equal to unity for both layers. The coherence between the electron states in the two layers is equivalent to the formation of excitons in a macroscopic coherent state. This makes it possible to compare the energy spectrum of collective elementary excitations of Bose-Einstein condensed excitons under conditions of the quantum Hall effect and coplanar magnetoexcitons. The breaking of the global gauge symmetry or of the continuous rotational symmetry leads to the formation of a gapless spectrum of the Nambu-Goldstone type, whereas the breaking of the local gauge symmetry is accompanied by the appearance of a gap in the energy spectrum (Higgs phenomenon). These phenomena are equivalent to the formation of massless and massive particles in the relativistic physics. The application of the Nielsen-Chadha theorem, which determines the number of Nambu-Goldstone modes as a function of the number of broken symmetry operators, is demonstrated using the example of Bose-Einstein condensation of spinor atomic gases in an optical trap. This example is presented for a better understanding of the results obtained in the case of a Bose-Einstein condensation of coplanar magnetoexcitons. The Higgs phenomenon leads to the formation of composite particles under conditions of the fractional quantum Hall effect. Their description is given in terms of the Ginzburg-Landau theory. The possibilities for the appearance of spontaneous coherence in a system of indirect excitons in structures with a double quantum well are analyzed. The experimental attempts to create these conditions, the main results obtained in this field, and the accumulated knowledge are reviewed. The basic properties of the energy spectrum of magnetoexciton polaritons in a microcavity are formulated. A hypothesis is put forward about the possibility of forming two-dimensional magnetoexcitons and two-dimensional magnetoexciton polaritons of high density with attached point quantum vortices, i.e., about the possibility of forming new composite particles.

Relation between high-energy quasiparticles of quasi-one-dimensional antiferromagnets in a magnetic field and a doublon of a Hubbard chain

In spin-1/2 one-dimensional Heisenberg antiferromagnets and anisotropic triangular Heisenberg antiferromagnets, high-energy states carrying considerable spectral weights have been observed in a magnetic field using inelastic neutron scattering. Such high-energy properties cannot be explained in terms of either Nambu-Goldstone bosons due to spontaneous breaking of continuous symmetries or quasiparticles in a Tomonaga-Luttinger liquid. Here, we show that the mechanism causing the high-energy states is analogous to that of the upper Hubbard band in the one-dimensional Hubbard model, by theoretically tracing the origin of the high-energy states back to string solutions of the Bethe ansatz.

Classification on the Average of Random Walks

During the last decade many attempts have been made to characterize absence of spontaneous breaking of continuous symmetry for the Heisenberg model on graphs by using suitable classifications of random walks (refs. 4 and 10). We propose and study a new type problem for random walks on graphs, which is particularly interesting for disordered graphs. We compare this classification with the classical one and with an analogous one introduced in ref. 4. Various examples, that are not space-homogeneous, are provided.

FUZZY NAMBU–GOLDSTONE PHYSICS

In space–time dimensions larger than 2, whenever a global symmetry G is spontaneously broken to a subgroup H, and G and H are Lie groups, there are Nambu–Goldstone modes described by fields with values in G/H. In two-dimensional space–times as well, models where fields take values in G/H are of considerable interest even though in that case there is no spontaneous breaking of continuous symmetries. We consider such models when the world sheet is a two-sphere and describe their fuzzy analogs for G = SU (N+1), H = S(U(N-1) ⊗ U (1)) ≃ U(N) and [Formula: see text]. More generally our methods give fuzzy versions of continuum models on S2when the target spaces are Grassmannians and flag manifolds described by (N+1) × (N+1) projectors of rank ≤ (N+1)/2. These fuzzy models are finite-dimensional matrix models which nevertheless retain all the essential continuum topological features like solitonic sectors. They seem well suited for numerical work.

Superconductivity with the meron-cluster algorithm

The meron-cluster algorithm was previously used to extensively study the physics associated with the spontaneous breaking of a discrete symmetry. We recently discovered that a larger class of models with spontaneous breaking of continuous symmetries can also be simulated using the meron-cluster algorithm. Here we study one of these new models which belongs to the attractive Hubbard model family. In particular we study the spontaneous breaking of the U(1) fermion number symmetry in two dimensions and find clear evidence for a Kosterlitz-Thouless transition to a superconducting phase.