Symmetry Breaking Phase Research Articles

Entropic Order Parameters for Categorical Symmetries in 2D-CFT

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (1+1)-d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of (1+1)-d theories with categorical symmetries.

Origin of Life: A Symmetry-Breaking Physical Phase Transition

The origin of life has previously been subject to numerous studies and hypotheses. Typically, related models focus on the emergence of chemical networks such as the RNA world or the Krebs energy cycle. Here, the onset of life is described as a symmetry-breaking kinetic phase transition. The novel symmetry of life is the arbitrariness of code that is fundamental to symbolic information processing, coining all forms of life from the very beginning. Symbols evolved from non-symbolic, structural information of the inanimate physical world. The responsible transition process was discovered a century ago in behavioural biology, regarded as ‘ritualisation’. The physical properties of this transition include neutral Lyapunov stability and critical fluctuations in the associated Goldstone modes. As a conceptual model, a hypothetical simple molecular ritualisation process is suggested, along with the emergent semiotics of symbolic information processing.

Topological flat bands in a family of multilayer graphene moiré lattices

Moiré materials host a wealth of intertwined correlated and topological states of matter, all arising from flat electronic bands with nontrivial quantum geometry. A prominent example is the family of alternating-twist magic-angle graphene stacks, which exhibit symmetry-broken states at rational fillings of the moiré band and superconductivity close to half filling. Here, we introduce a second family of twisted graphene multilayers made up of twisted sheets of M- and N-layer Bernal-stacked graphene flakes. Calculations indicate that applying an electric displacement field isolates a flat and topological moiré conduction band that is primarily localized to a single graphene sheet below the moiré interface. Phenomenologically, the result is a striking similarity in the hierarchies of symmetry-broken phases across this family of twisted graphene multilayers. Our results show that this family of structures offers promising new opportunities for the discovery of exotic new correlated and topological phenomena, enabled by using the layer number to fine tune the flat moiré band and its screening environment.

Mapping the nonequilibrium order parameter of a quasi-two dimensional charge density wave system

The driving force of a charge density wave (CDW) transition in quasi-two dimensional systems is still debated, while being crucial in understanding electronic correlation in such materials. Here we use femtosecond time- and angle-resolved photoemission spectroscopy combined with computational methods to investigate the coherent lattice dynamics of a prototypical CDW system. The photo-induced temporal evolution of the periodic lattice distortion associated with the amplitude mode reveals the dynamics of the free energy functional governing the order parameter. Our approach establishes that optically-induced screening rather than CDW melting at the electronic level leads to a transiently modified potential which explains the anharmonic behaviour of the amplitude mode and discloses the structural origin of the symmetry-breaking phase transition.

Activity Unmasks Chirality in Liquid-Crystalline Matter

Active matter theories naturally describe the mechanics of living systems. As biological matter is overwhelmingly chiral, an understanding of the implications of chirality for the mechanics and statistical mechanics of active materials is a priority. This article examines active, chiral materials from a liquid-crystal physicist's point of view, extracting general features of broken-symmetry-ordered phases of such systems without reference to microscopic details. Crucially, this demonstrates that activity allows chirality to affect the hydrodynamics of broken-symmetry phases in contrast to passive liquid crystals, in which chirality induces the formation of a range of spatially periodic structures whose large-scale mechanics have no signatures of broken parity symmetry. In active systems, chirality leads to the formation of phases that break time translation symmetry, which is impossible in equilibrium, and the existence of new kinds of elastic force densities in translation symmetry-broken states.

Pseudo-easy-axis anisotropy in antiferromagnetic S=1 diamond-lattice systems

We investigate the magnetic properties of S=1 antiferromagnetic diamond-lattice, NiX2(pyrimidine)2 (X=Cl, Br), hosting a single-ion anisotropy (SIA) orientation which alternates between neighboring sites. Through neutron diffraction measurements of the X=Cl compound, the ordered state spins are found to align collinearly along a pseduo-easy axis, a unique direction created by the intersection of two easy planes. Similarities in the magnetization, exhibiting spin-flop transitions, and the magnetic susceptibility in the two compounds imply that the same magnetic structure and a pseduo-easy axis is also present for X=Br. We estimate the Hamiltonian parameters by combining analytical calculations and Monte Carlo (MC) simulations of the spin-flop and saturation field. The MC simulations also reveal that the spin-flop transition occurs when the applied field is parallel to the pseduo-easy axis. Contrary to conventional easy-axis systems, there exist field directions perpendicular to the pseduo-easy axis for which the magnetic saturation is approached asymptotically and no symmetry-breaking phase transition is observed at finite fields. Published by the American Physical Society 2024

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.

Symmetry, magnetic transitions and multiferroic properties of B-site-ordered A2MnB'O6 perovskites (B' = [Co, Ni]).

The presence of magnetic atoms at the A and B sites and the coupling between these two spin subsystems in perovskites gives rise to a variety of exciting effects. In particular this coupling attracts interest from the field of novel multiferroic and magnetoelectric oxides. Moreover, magnetic double perovskites presenting cationic order at the B sites incorporate an additional modulation that can favor symmetry breaking, multiferroic, magnetoelectric and polar phases. Here, we describe the magnetic structures obtained from neutron diffraction and analyze the symmetry properties of well ordered A2MnB'O6 double perovskites with A= Lu, Yb, Tm, Er, Ho, Y, Tb, La0.5Tb0.5, La and B' = Co or Ni. A rich variety of magnetic orders is formed that have been identified and described, and their symmetry properties are discussed in relation to the multiferroic and magnetoelectric properties of the different compounds.

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.