Fermion interactions in models with strong Wilson-Yukawa couplings

Characterization of the ground states of a simplified CuO2 model in strong- and weak-coupling regions

In a recent paper a toy model (hypercubic model) undergoing a first-order -symmetry-breaking phase transition (-SBPT) was introduced. The hypercubic model was inspired by the topological hypothesis, according to which a phase transition may be entailed by suitable topological changes of the equipotential surfaces (Σv’s) of configuration space. In this paper we show that at the origin of a -SBPT there is a geometric property of the Σv’s, i.e. dumbbell-shaped Σv’s suitably defined, which includes a topological change as a limiting case. This property is necessary and sufficient condition to entail a -SBPT. This new approach has been applied to three models: a modified version introduced here of the hypercubic model, a model introduced in a recent paper with a continuous -SBPT belonging to several universality classes, and finally to a physical models, i.e. the mean-field ϕ4 model and a simplified version of it.

There is considerable interest in the dynamics of topological defects formed during a symmetry breaking phase transition in fields as diverse as condensed matter physics, particle physics and cosmology. Liquid crystals, with their many symmetry breaking phase transitions are ideal materials for such studies. Here we report on light transmission studies of the coarsening of three-dimensional defect tangles in uniaxial nematic liquid crystals subjected to a sudden pressure jump from the isotropic phase to the nematic phase. We have verified that the type 1/2 disclination line density, as a function of time, scales as t−v with v = 1.0 ± 0.1 over four decades in time. The transmitted light intensity exhibits two distinct scaling regimes depending on whether propagation without scattering or diffusive propagation with multiple scattering dominates the light reaching the detector.

The q-state clock model, sometimes called the discrete XY model, is known to show a second-order (symmetry-breaking) phase transition in two dimensions for q≤4 (q=2 corresponds to the Ising model). On the other hand, the q→∞ limit of the model corresponds to the XY model, which shows the infinite order (non-symmetry-breaking) Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two dimensions. Interestingly, the two-dimensional clock model with q≥5 is predicted to show three different phases and two associated phase transitions. There are varying opinions about the actual characters of phases and the associated transitions. In this work, we develop the basic and higher-order mean-field (MF) theories to study the q-state clock model systematically. Our MF calculations reaffirm that, for large q, there are three phases: (broken) Z_{q} symmetric ferromagnetic phase at the low temperature, emergent U(1) symmetric BKT phase at the intermediate temperature, and paramagnetic (disordered) phase at the high temperature. The phase transition at the higher temperature is found to be of the BKT type, and the other transition at the lower temperature is argued to be a large-order spontaneous symmetry-breaking type (the largeness of transition order yields the possibility of having some of the numerical characteristics of a BKT transition). The higher-order MF theory developed here better characterizes phases by estimating the spin-spin correlation between two neighbors.

Depending on the parity of the rotational quantum number J, solid hydrogens exhibit either pressure-driven broken symmetry phase (BSP) transitions (even-J species – para-hydrogen (p-H2), and ortho-deuterium (o-D2)) or usual order-disorder phase transitions (odd-J species – o-H2 and p-D2) with the phase transition temperature increasing monotonically with pressure from the phase transition point at zero pressure. At the same time, for solid HD the BSP phase transition line displays a minimum, indicating that the disordered phase is reentrant. In this work a model of quantum linear rotors is used to study characteristic features of the P–T phase diagrams for ortho–para mixtures in solid H2 and D2. We developed a mean-field theory of even-J – odd-J mixtures of quantum linear rotors on a 3D lattice. Two limiting cases are considered: mixtures at thermodynamic equilibrium, where the conversion time is small or comparable with the thermalization time, and the opposite case, frozen mixtures, when the conversion time is large compared with other relevant times. We found that for all equilibrium linear rotor systems — the even-J – odd-J mixtures — the reentrant behavior of the phase transition lines is an entropy-driven phenomenon, as was previously found for the all-J system. Experimentally, conditions to find the reentrant BSP transition line are most favorable for H2 mixtures, whereas the frozen monotonic phase lines should be the case for D2 even-J – odd-J mixtures. These results may therefore be particularly useful for understanding the anomalous transition region of the BSP transition documented for D2 mixtures.

We study the influence of random anisotropy type quenched disorder on the phase behavior of the system, which exhibits in undistorted case the 2nd order continuous symmetry breaking phase transition. Invoking the central limit theorem we express the free energy of the system in terms of the order parameter η and the characteristic length ξ of the gauge field ϕ. The latter exhibits the Goldstone fluctuation mode and is consequently extremely susceptible to the imposed disorder. In case of negligible distribution width ΔT of the local transition temperatures the disorder converts the 2nd order transition into a discontinuous one for W<WC, where Wrepresents the disorder strength. Above the critical disorder strength WC the transition becomes gradual. However for the finite width ΔT the transition becomes gradual for any W>0. We demonstrate that for large enough values of ΔT the system behavior is dominated by the distribution of temperatures, while the details of the random field interaction term play a secondary role. The influence of distribution of local (quasi) phase transitions is in most theoretical approaches dealing with randomly perturbed systems neglected from the outset.

With a general mixing of vector and scalar couplings in a two-dimensional world, a short-range potential is used to explore certain features of the bound states of a spinless particle. Bound-state solutions are found in terms of the Gauss hypergeometric series when the potential parameters obey a certain constraint relation limiting the dosage of a vector coupling. The appearance of the Schiff–Snyder–Weinberg effect for a strong vector coupling and a short-range potential as well as its suppression by the addition of a scalar coupling is discussed.

The observation of genuine quantum effects in systems governed by non-Hermitian Hamiltonians has been an outstanding challenge in the field. Here we simulate the evolution under such Hamiltonians in the quantum regime on a superconducting quantum processor by using a dilation procedure involving an ancillary qubit. We observe the parity–time ({mathcal{PT}})-symmetry breaking phase transition at the exceptional points, obtain the critical exponent, and show that this transition is associated with a loss of state distinguishability. In a two-qubit setting, we show that the entanglement can be modified by local operations.

Our understanding of the mechanism by which topological defects are formed in symmetry breaking phase transitions has recently changed. We examine the non-equilibrium dynamics of defect formation for weakly-coupled global O(N) theories possessing vortices (strings) and monopoles. It is seen that, as domains form and grow, defects are swept along on their boundaries at a density of about one defect per coherence area (strings) or per coherence volume (monopoles).

In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field ϕ^{4} model with a Z_{2} symmetry. Our purpose is discovering, if any, the relation between the second-order Z_{2}-symmetry-breaking phase transition and the geometric entities mentioned above. The mean-field interaction allows us to solve analytically either the thermodynamic in the canonical ensemble or the topology by means of Morse theory. We have analyzed the results in the light of two theorems on sufficiency conditions for symmetry-breaking phase transitions recently proven. This study is part of a research line based on the general framework of geometric-topological approach to Hamiltonian chaos and critical phenomena.

The paper is devoted to the memory of Dmitry Diakonov. We discuss gravity emerging in the fermionic vacuum as suggested by Diakonov 10 years ago in his paper “Towards lattice-regularized Quantum Gravity”. [1] Gravity emerges in the phase transition. The order parameter in this transition is the tetrad field e^a_mu, which appears as the bilinear composite of the fermionic fields. The similar scenario of the symmetry breaking takes place in the B-phase of superfluid ^3He, where the real part of the spin-triplet p-wave order parameter matrix A_{a i} plays the role of the emerging tetrad (triad). In Diakonov theory this symmetry breaking gives 6 Nambu-Goldstone modes; 6 gauge bosons in the spin-connection fields, which absorb 6 NG modes and become massive gauge bosons; and 6 Higgs fields. In ^3He-B, these Higgs collective modes correspond to 6 massive gravitons, while in the emerging general relativity the Higgs collective modes give rise to two massless gravitational waves.

Complex pattern formation is commonly observed in spatially extended, continuous, dissipative systems which are driven far from equilibrium by an external stress. Under the influence of this stress, the system can undergo a series of symmetry breaking bifurcations or phase transitions and the resulting patterns become more and more complicated, both temporally and spatially, as the stress is increased. This chapter illustrates the rich variety of pattern forming instability mechanisms in wide aperture lasers, using the two-level and Raman single longitudinal mode lasers as prototype systems. It shows that the Maxwell-Bloch laser equations admit an exact finite amplitude traveling wave solution for positive detuning of the laser and also admit a transverse spatially homogeneous solution for negative detuning. The chapter introduces the laser models, compare and contrast their physical characteristics and briefly review their bifurcation behavior. 1D wide aperture lasers are expected to exhibit fundamentally different spatio-temporal behavior.

Despite the discovery of a Higgs boson $h$ (125 GeV) at the LHC run 1, its self-interaction has fully evaded direct experimental probe so far. Such self-interaction is vital for electroweak symmetry breaking, vacuum stability, and electroweak phase transition. It is a most likely place to encode new physics beyond the standard model. We parametrize such new physics by model-independent dimension-six effective operators and study their tests via Higgs pair production at hadron colliders. We analyze three major di-Higgs production channels at the parton level and compare the parameter dependence of total cross sections and kinematic distributions at the LHC (14 TeV) and $pp$ (100 TeV) hadron collider. We further perform full simulations for the di-Higgs production channel $gg\ensuremath{\rightarrow}hh\ensuremath{\rightarrow}b\overline{b}\ensuremath{\gamma}\ensuremath{\gamma}$ and its backgrounds at the $pp$ (100 TeV) hadron collider. We construct four kinds of benchmark points and study the sensitivities to probing different regions of the parameter space of cubic Higgs interactions. We find that for a one-parameter analysis and with a $3\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ ($30\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$) integrated luminosity, the $gg\ensuremath{\rightarrow}hh\ensuremath{\rightarrow}b\overline{b}\ensuremath{\gamma}\ensuremath{\gamma}$ channel can measure the SM cubic Higgs coupling and the derivative cubic Higgs coupling to an accuracy of about 13% (4.2%) and 5% (1.6%), respectively.

We demonstrate symmetry-selective control of nonlinear photoconductivity in monolayer MoSe2, where near-resonant, linearly polarized light induces transition-specific symmetry breaking and topological phase transitions without violating time-reversal symmetry. Combining Floquet theory with first-principles modeling, we show that x-polarized light breaks both the threefold rotation C3 and the antiunitary mirror $${\mathcal{T}}{M}_{x}$$, whereas y-polarized light preserves $${\mathcal{T}}{M}_{x}$$, enabling polarization-resolved generation of interband Berry curvature dipoles. This selective symmetry breaking yields a circular photogalvanic current whose direction and magnitude are tunable via the pump frequency, offering a direct ultrafast probe of Floquet-induced band inversion. These findings establish a viable pathway for detecting light-driven topological currents in nonchiral two-dimensional semiconductors and advancing terahertz optoelectronic applications.

The precise manipulation of electronic properties through the introduction of foreign atoms—doping—remains the central paradigm of condensed matter physics and the foundational technology of the information age. From the early formulation of rigid-band semiconductor theory to the contemporary exploration of quantum materials, the physics of doping has evolved from a perturbative treatment of impurities to a complex study of thermodynamic self-regulation, symmetry breaking, and topological phase transitions.1While the twentieth century was defined by the mastery of covalent semiconductors like silicon (Si) and gallium arsenide (GaAs), where dopants act as simple hydrogenic centers, the current frontier involves