Symmetry Breaking Phase Research Articles

Experimental realization of on-chip few-photon control around exceptional points.

Non-Hermitian physical systems have attracted considerable attention in recent years for their unique properties around exceptional points (EPs), where the eigenvalues and eigenstates of the system coalesce. Phase transitions near exceptional points can lead to various interesting phenomena, such as unidirectional wave transmission. However, most of those studies are in the classical regime and whether these properties can be maintained in the quantum regime is still a subject of ongoing studies. Using a non-Hermitian on-chip superconducting quantum circuit, here we observe a phase transition and the corresponding exceptional point between the two phases. Furthermore, we demonstrate that unidirectional microwave transmission can be achieved even in the few-photon regime within the broken symmetry phase. This result holds some potential applications, such as on-chip few-photon microwave isolators. Our study reveals the possibility of exploring the fundamental physics and practical quantum devices with non-Hermitian systems based on superconducting quantum circuits.

Suppression of symmetry-breaking correlated insulators in a rhombohedral trilayer graphene superlattice.

Counterintuitive temperature dependence of isospin flavor polarization has recently been found in twisted bilayer graphene, where unpolarized electrons in a Fermi liquid become a spin-valley polarized insulator upon heating. So far, the effect has been limited to v = +/-1 (one electron/hole per superlattice cell), leaving open questions such as whether it is a general property of symmetry-breaking electronic phases. Here, by studying a rhombohedral trilayer graphene/boron nitride moiré superlattice, we report that at v = -3 a resistive peak emerges at elevated temperatures or in parallel magnetic fields. Concomitantly, the Hall carrier density tends to reset at the integer filling, signaling spin-valley flavor symmetry breaking. These phenomena can also be observed at v = -1 and -2 when the displacement field is large enough to suppress correlated insulators at low temperatures. Our results greatly expand the scope for observing the counterintuitive temperature dependence of flavor polarization, i.e., the regimes proximal to symmetry-breaking phases where the flavor polarization order strongly fluctuates, encouraging more experimental and theoretical exploration of isospin flavor polarization dynamics in flat-band moiré systems.

Polymorphic transition of solid deuterium into broken symmetry phase: Application of Mayer group expansion method

Polymorphic transition of solid deuterium into broken symmetry phase: Application of Mayer group expansion method

On the Use of Reflection Polarized Optical Microscopy for Rapid Comparison of Crystallinity and Phase Segregation of P3HT:PCBM Thin Films.

Rapid, nondestructive characterization techniques for evaluating the degree of crystallinity and phase segregation of organic semiconductor blend thin films are highly desired for in-line, automated optoelectronic device fabrication facilities. Here, it is demonstrated that reflection polarized optical microscopy (POM), a simple technique capable of imaging local anisotropy of materials, is capable of determining the relative degree of crystallinity and phase segregationof thin films of polymer:fullerene blends. While previous works on POM of organic semiconductors have largely employed the transmission geometry, it is demonstrated that reflection POM provides 3× greater contrast. The optimal configuration is described to maximize contrast from POM images of polymer:fullerene films, which requires Köhler illumination and slightly uncrossed polarizers, with an uncrossing angle of ±3°. It is quantitatively demonstrated that contrast in POM images directly correlates with 1) the degree of polymer crystallinity and 2) the degree of phase segregation between polymer and fullerene domains. The origin of the bright and dark domains in POM is identified as arising from symmetry-broken liquid crystalline phases (i.e., dark conglomerates), and it is proven that they have no correlation with surface topography. The use of reflection POM as a rapid diagnostic tool for automated device fabrication facilities is discussed.

Spin reorientation and the interplay of magnetic sublattices in Er2CuMnMn4O12.

Through a combination of magnetic susceptibility, specific heat, and neutron powder diffraction measurements we have revealed a sequence of four magnetic phase transitions in the columnar quadruple perovskite Er2CuMnMn4O12. A key feature of the quadruple perovskite structural framework is the complex interplay of multiple magnetic sublattices via frustrated exchange topologies and competing magnetic anisotropies. It is shown that in Er2CuMnMn4O12, this phenomenology gives rise to multiple spin-reorientation transitions driven by the competition of easy-axis single ion anisotropy and the Dzyaloshinskii-Moriya interaction; both within the manganese B-site sublattice. At low temperature, one Er sublattice orders due to a finite f-d exchange field aligned parallel to its Ising axis, while the other Er sublattice remains non-magnetic until a final, symmetry-breaking phase transition into the ground state. This non-trivial low-temperature interplay of transition metal and rare-earth sublattices, as well as an observed k = (0, 0, ½) periodicity in both manganese spin canting and Er ordering, raises future challenges to develop a complete understanding of the R2CuMnMn4O12 family.

Quantum phases and transitions in spin chains with non-invertible symmetries

Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are implemented by transformations that do not form a group. Such symmetries appear in large families of gapless states of quantum matter and constrain their low-energy dynamics. To provide a UV-complete description of such symmetries, it is useful to construct lattice models that respect these symmetries exactly. In this paper, we discuss two families of one-dimensional lattice Hamiltonians with finite on-site Hilbert spaces: one with (invertible) S_3S3 symmetry and the other with non-invertible \mathsf{Rep}(S_3)𝖱𝖾𝗉(S3) symmetry. Our models are largely analytically tractable and demonstrate all possible spontaneous symmetry breaking patterns of these symmetries. Moreover, we use numerical techniques to study the nature of continuous phase transitions between the different symmetry-breaking gapped phases associated with both symmetries. Both models have self-dual lines, where the models are enriched by so-called intrinsically non-invertible symmetries generated by Kramers-Wannier-like duality transformations. We provide explicit lattice operators that generate these non-invertible self-duality symmetries. We show that the enhanced symmetry at the self-dual lines is described by a 2+1d symmetry-topological-order (SymTO) of type JK_4\boxtimes \overline{JK}_4JK4⊠JK¯4. The condensable algebras of the SymTO determine the allowed gapped and gapless states of the self-dual S_3S3-symmetric and \mathsf{Rep}(S_3)𝖱𝖾𝗉(S3)-symmetric models.

Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids.

We investigate the nature of the topological quantum phase transition between the gapless and gapped Kitaev quantum spin liquid phases away from the exactly solvable point. The transition is driven by anisotropy of the Kitaev couplings. At the critical point, the two Dirac points of the gapless Majorana modes merge, resulting in the formation of a semi-Dirac point with quadratic and linear band touching directions. We derive an effective Gross-Neveu-Yukawa-type field theory that describes the topological phase transition in the presence of additional magnetic interactions. We obtain the infrared scaling form of the propagator of the dynamical Ising order parameter field and perform a renormalization-group analysis. The universality of the transition is found to be different from that of symmetry-breaking phase transitions of semi-Dirac electrons. However, as in the electronic case, the Majorana fermions acquire an anomalous dimension, indicative of the breakdown of the fractionalized quasiparticle description.

Exotic spin-Hall effect in non-Hermitian optical systems

Abstract We systematically explore the origin and evolution of the exceptional points (EP) when a light beam is scattered by a parity-time (PT)-symmetric system using a scattering matrix approach and a full-wave theory. It is demonstrated that the PT-symmetric system switches between symmetry and symmetry-breaking phases at the EPs, giving rise to singular features in the Fresnel coefficients and causing the spin-Hall effect (SHE) near the EPs to exhibit anomalous features such as significantly enhanced transverse spin-Hall shifts and additional in-plane spin-Hall shifts. This exotic SHE can be explained by the significant beam intensity distortion caused by the destructive interference between the spin-maintained normal modes and the spin-reversed abnormal modes in the scattered light. This phenomenon can further be understood in terms of vortex mode decomposition, wherein it can be interpreted as the competition and superposition of three vortex modes with topological charges of −1, 0, and 1, respectively. These findings elucidate the mechanism of the unusual SHE around the EPs and offer potential avenues for EP-based sensing and structured light manipulation.

Antiscreening and Nonequilibrium Layer Electric Phases in Graphene Multilayers.

Screening is a ubiquitous phenomenon through which the polarization of bound or mobile charges tends to reduce the strengths of electric fields inside materials. Here, we show how photoexcitation can be used as a knob to transform conventional out-of-plane screening into antiscreening-the amplification of electric fields-in multilayer graphene. We find that, by varying the photoexcitation intensity, multiple nonequilibrium screening regimes can be accessed, including near-zero screening, antiscreening, and overscreening (reversing electric fields). Strikingly, at modest continuous wave photoexcitation intensities, the nonequilibrium polarization states become multistable, hosting light-induced ferroelectriclike steady states with nonvanishing out-of-plane polarization (and band gaps) even in the absence of an externally applied displacement field in nominally inversion symmetric stacks. This rich phenomenology reveals a novel paradigm of dynamical quantum matter that we expect will enable a variety of nonequilibrium broken symmetry phases.

Symmetry breaking and non-ergodicity in a driven-dissipative ensemble of multilevel atoms in a cavity

Dissipative light-matter systems can display emergent collective behavior. Here, we report a Z2-symmetry-breaking phase transition in a system of multilevel Rb87 atoms strongly coupled to a weakly driven two-mode optical cavity. In the symmetry-broken phase, nonergodic dynamics manifests in the emergence of multiple stationary states with disjoint basins of attraction. This feature enables the amplification of a small atomic population imbalance into a characteristic macroscopic cavity transmission signal. Our experiment does not only showcase strongly dissipative atom-cavity systems as platforms for probing nontrivial collective many-body phenomena, but also highlights their potential for hosting technological applications in the context of sensing, density classification, and pattern retrieval dynamics within associative memories. Published by the American Physical Society 2024

Superconductivity and Mott Physics in Organic Charge Transfer Materials.

The phase diagrams of quasi two-dimensional organic superconductors display a plethora of fundamental phenomena associated with strong electron correlations, such as unconventional superconductivity, metal-insulator transitions, frustrated magnetism and spin liquid behavior. We analyze a minimal model for these compounds, the Hubbard model on an anisotropic triangular lattice, using cutting-edge quantum embedding methods respecting the lattice symmetry. We demonstrate the existence of unconventional superconductivity by directly entering the symmetry-broken phase. We show that the crossover from the Fermi liquid metal to the Mott insulator is associated with the formation of a pseudogap. The predicted momentum-selective destruction of the Fermi surface into hot and cold regions provides motivation for further spectroscopic studies. Our theoretical results agree with experimental phase diagrams of κ-BEDT organics.

Coexisting Charge Density Waves in Twisted Bilayer NbSe2.

Twisted bilayers of 2D materials have emerged as a tunable platform for studying broken symmetry phases. While most interest has been focused toward emergent states in systems whose constituent monolayers do not feature broken symmetry states, assembling monolayers that exhibit ordered states into twisted bilayers can also give rise to interesting phenomena. Here, we use first-principles density-functional theory calculations to study the atomic structure of twisted bilayer NbSe2 whose constituent monolayers feature a charge density wave. We find that different charge density wave states coexist in the ground state of the twisted bilayer: monolayer-like 3 × 3 triangular and hexagonal charge density waves are observed in low-energy stacking regions, while stripe charge density waves are found in the domain walls surrounding the low-energy stacking regions. These predictions, which can be tested by scanning tunneling microscopy experiments, highlight the potential to create complex charge density wave ground states in twisted bilayer systems.

The cosmological constant problem and the effective potential of a gravity-coupled scalar

We consider a quantum scalar field in a classical (Euclidean) De Sitter background, whose radius is fixed dynamically by Einstein’s equations. In the case of a free scalar, it has been shown by Becker and Reuter that if one regulates the quantum effective action by putting a cutoff N on the modes of the quantum field, the radius is driven dynamically to infinity when N tends to infinity. We show that this result holds also in the case of a self-interacting scalar, both in the symmetric and broken-symmetry phase. Furthermore, when the gravitational background is put on shell, the quantum corrections to the mass and quartic self-coupling are found to be finite.

Anisotropic magnetic and quadrupolar H−T phase diagram of CeRh2As2

The tetragonal heavy-fermion compound CeRh2As2 has intriguing low-temperature symmetry-breaking phases whose nature is unclear. The unconventional superconducting phase is complemented by other normal-state phases which presumably involve ordering of 4f electron multipoles supported by the Kramers doublets split by the tetragonal crystal electric field (CEF). The most striking aspect is the pronounced anisotropic H−T phase boundary for in-plane and out-of plane field directions. Using a localized 4f CEF model we demonstrate that its essential features can be understood as the result of competing low-field easy-plane magnetic order and field-induced quadrupolar order of xy type. We present calculations based on coupled multipole random phase approximation response function approach as well as molecular field treatment in the ordered regime. We use an analytical approach for a reduced quasiquartet model and numerical calculations for the complete CEF level scheme. We discuss the quantum critical properties as function of multipolar control parameters and explain the origin of a pronounced ac anisotropy of the H−T phase diagram. Finally, the field and temperature evolution of multipolar order parameters is derived and the high-field phase diagram is predicted. Published by the American Physical Society 2024

Scalar field perturbation of hairy black holes in EsGB theory

We investigate scalar field perturbations of the hairy black holes involved with spontaneous symmetry breaking of the global U(1) symmetry in Einstein-scalar-Gauss-Bonnet theory for asymptotically flat spacetimes. We consider the mechanism that black holes without hairs become unstable at the critical point of the coupling constant and undergo a phase transition to hairy black holes in the symmetry-broken phase driven by spontaneous symmetry breaking. This transition occurs near the black hole horizon due to the diminishing influence of the Gauss-Bonnet term at infinity. To examine such process, we introduce a scalar field perturbation on the newly formed background spacetime. We solve the linearized perturbation equation using Green’s function method. We begin by solving the Green’s function, incorporating the branch cut contribution. This allows us to analytically investigate the late-time behavior of the perturbation at both spatial and null infinity. We found that the late-time behavior only differs from the Schwarzschild black hole by a mass term. We then proceed to calculate the quasinormal modes (QNMs) numerically, which arise from the presence of poles in the Green’s function. Our primary interest lies in utilizing QNMs to investigate the stability of the black hole solutions both the symmetric and symmetry-broken phases. Consistent with the prior study, our analysis shows that hairy black holes in the symmetric phase become unstable when the quadratic coupling constant exceeds a critical value for a fixed value of the quartic coupling constant. In contrast, hairy black holes in the symmetry-broken phase are always stable at the critical value. These numerical results provide strong evidence for a dynamical process that unstable black holes without hairs transition into stable hairy black holes in the symmetry-broken phase through the spontaneous symmetry breaking.

Complexity and operator growth for quantum systems in dynamic equilibrium

Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a PT-symmetric system of oscillators, which exhibits two phase transitions that separate a dissipative state, a Rabi-oscillation state, and an ultra-strongly coupled regime. We use a generalization of the su(1) algebra associated to the Bateman oscillator to describe the Hamiltonian of the coupled system, and construct a set of coherent states associated with this algebra. We compute the Krylov (spread) complexity using these coherent states, and find that it can distinguish between the PT-symmetric and PT symmetry-broken phases. We also show that the Krylov complexity reveals the ill-defined nature of the vacuum of the Bateman oscillator, which is a special case of our system. Our results demonstrate the utility of Krylov complexity as a tool to probe the properties and transitions of PT-symmetric systems.

Nanomechanically-induced nonequilibrium quantum phase transition to a self-organized density wave of a Bose-Einstein condensate

We report on a nonequilibrium quantum phase transition (NQPT) in a hybrid quantum many-body system consisting of a vibrational mode of a damped nanomembrane interacting optomechanically with a cavity, whose output light couples to two internal states of an ultracold Bose gas held in an external quasi-one-dimensional box potential. For small effective membrane-atom couplings, the system is in a homogeneous Bose-Einstein condensate (BEC) steady state, with no membrane displacement. Depending on the transition frequency between the two internal atomic states, either one or both internal states are occupied. By increasing the atom-membrane couplings, the system transitions to a symmetry-broken self-organized BEC phase, which is characterized by a considerably displaced membrane steady-state and density-wave-like BEC profiles. This NQPT can be both discontinuous and continuous for a certain interval of transition frequencies and is purely discontinuous outside of it. Published by the American Physical Society 2024

Candidate for a Passively Protected Quantum Memory in Two Dimensions.

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a "passively protected quantum memory," defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is known only in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model, the photonic-Ising model, which appears to passively correct against both bit-flip and phase-flip errors in two dimensions: a square lattice composed of photonic "cat qubits" coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z_{2}-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips. We also discuss possible ways to realize the photonic-Ising model.

Van Hove annihilation and nematic instability on a kagome lattice.

A nematic phase breaks the point-group symmetry of the crystal lattice and is known to emerge in correlated materials. Here we report the observation of an intra-unit-cell nematic order and associated Fermi surface deformation in the kagome metal ScV6Sn6. Using scanning tunnelling microscopy and scanning tunnelling spectroscopy, we reveal a stripe-like nematic order breaking the crystal rotational symmetry within the kagome lattice itself. Moreover, we identify a set of Van Hove singularities adhering to the kagome-layer electrons, which appear along one direction of the Brillouin zone and are annihilated along other high-symmetry directions, revealing rotational symmetry breaking. Via detailed spectroscopic maps, we further observe an elliptical deformation of the Fermi surface, which provides direct evidence for an electronically mediated nematic order. Our work not only bridges the gap between electronic nematicity and kagome physics but also sheds light on the potential mechanism for realizing symmetry-broken phases in correlated electron systems.

Nambu-covariant many-body theory II: Self-consistent approximations

The theory of Self-Consistent Green’s Function (SCGF) is reformulated in an explicit Nambu-covariant fashion for applications to many-body systems at non-zero temperature in symmetry-broken phases. This is achieved by extending the Nambu-covariant formulation of perturbation theory, presented in the first part of this work, to non-perturbative schemes based on self-consistently dressed propagators and vertices. We work out in detail the self-consistent ladder approximation, motivated by a trade-off between numerical complexity and many-body phenomenology. Taking a complex general Hartree–Fock–Bogoliubov (HFB) propagator as a starting point, we also formulate and prove a sufficient condition on the stability of the HFB self-energy to ensure the convergence of the initial series of ladders at any energy. The self-consistent ladder approximation is written purely in terms of spectral functions and the resulting set of equations, when expressed in terms of Nambu tensors, are remarkably similar to those in the symmetry-conserving case. This puts the application of the self-consistent ladder approximation to symmetry-broken phases of infinite nuclear matter within reach.