The Symmetry Principle in Condensed Matter Physics (I)

Abstract

Symmetry distills the simplicity of natural laws from the complexity of physical phenomena. The symmetry principle is of vital importance in various aspects of modern physics, including analyzing atomic spectra, determining fundamental interactions in the Standard Model, and unifying physics at different energy scales. In this chapter, novel applications of this principle are reviewed in condensed matter physics and cold atom physics for exploring new states of matter.

References in corpus (96)

• Berry Phase Effects on Electronic Properties
• Photonic Floquet Topological Insulators
• Classification of topological quantum matter with symmetries
• Topological Crystalline Insulators
• Floquet Topological Insulator in Semiconductor Quantum Wells
• How to detect fluctuating order in the high-temperature superconductors
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Quantum Time Crystals
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Dirac Semimetals in Two Dimensions
• Nematic Fermi Fluids in Condensed Matter Physics
• Discrete time crystals: rigidity, criticality, and realizations
• Fractons
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Absence of Quantum Time Crystals
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• Quantum Theory of a Nematic Fermi Fluid
• A one-dimensional liquid of fermions with tunable spin
• Valley contrasting chiral phonons in monolayer hexagonal lattices
• Hourglass Fermions
• The Physics of Pair Density Waves
• Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon
• Classical Time Crystals
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Modeling spontaneous breaking of time-translation symmetry
• Exact SO(5) Symmetry in spin 3/2 fermionic system
• Topological singularities and the general classification of Floquet-Bloch systems
• Precise determination of ${}^6$Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules
• Impossibility of Spontaneously Rotating Time-Crystals: A No-Go Theorem
• Realization of SU(2)*SU(6) Fermi System
• SO(5) Theory of Antiferromagnetism and Superconductivity
• Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
• Floquet generation of Majorana end modes and topological invariants
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• In situ observation of strongly interacting ferromagnetic domains in a shaken optical lattice
• Topology and Broken Symmetry in Floquet Systems
• Color Superfluidity and "Baryon" Formation in Ultracold Fermions
• Fermi liquid instabilities in the spin channel
• Degenerate Fermi Gas of ${}^{87}$Sr
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Observation of a many-body-localized discrete time crystal with a programmable spin-based quantum simulator
• 1D Many-body localized Floquet systems II: Symmetry-Broken phases
• Exact SO(8) Symmetry in the Weakly-Interacting Two-Leg Ladder
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Competing orders in one dimensional spin 3/2 fermionic systems
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Quantum degenerate mixtures of alkali and alkaline-earth-like atoms
• Parity-breaking phases of spin-orbit-coupled metals with gyrotropic, ferroelectric and multipolar orders
• Floquet second-order topological insulators from nonsymmorphic space-time symmetries
• A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd${}_2$Re${}_2$O${}_7$
• Filling-Enforced Gaplessness in Band Structures of the 230 Space Groups
• Interaction and filling induced quantum phases of dual Mott insulators of bosons and fermions
• Dynamic generation of spin orbit coupling
• Floquet topological phases protected by time glide symmetry
• Confinement and Superfluidity in one-dimensional Degenerate Fermionic Cold Atoms
• Pairing of Fermions with Arbitrary Spin
• Coherent multi-flavour spin dynamics in a fermionic quantum gas
• Trionic phase of ultracold fermions in an optical lattice: A variational study
• Resonating plaquette phases in large spin cold atom systems
• Competing orders in the 2D half-filled SU(2N) Hubbard model through the pinning field quantum Monte-Carlo simulations
• Space-time crystal and space-time group
• Charge-$4e$ superconductivity from multi-component nematic pairing: Application to twisted bilayer graphene
• Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions
• Unconventional metamagnetic electron states in orbital band systems
• Vortex configurations of bosons in an optical lattice
• Inelastic collisions and density-dependent excitation suppression in a ${}^{87}$Sr optical lattice clock
• Bose-Einstein Condensation of ${}^{88}$Sr Through Sympathetic Cooling with ${}^{87}$Sr
• Exact spontaneous plaquette ground states for high-spin ladder models
• Spin conservation and Fermi liquid near a ferromagnetic quantum critical point
• Plaquette Ground State in the Two-dimensional SU(4) Spin-Orbital Model
• Exotic many-body physics with large-spin Fermi gases
• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry
• Charge instabilities at the metamagnetic transition
• Liquids in multi-orbital SU(N) Magnets with Ultracold Alkaline Earth Atoms
• Resonating singlet valence plaquettes
• Exactly solvable model for isospin S=3/2 fermionic atoms on an optical lattice
• Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model
• Evidence of an improper displacive phase transition in Cd${}_2$Re${}_2$O${}_7$ via time-resolved coherent phonon spectroscopy
• Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases
• Floquet-Bloch Oscillations and Intraband Zener Tunneling in an Oblique Spacetime Crystal
• Interaction effects with varying $N$ in SU($N$) symmetric fermion lattice systems
• Quintet pairing and non-Abelian vortex string in spin-3/2 cold atomic systems
• Resolved atomic interaction sidebands in an optical clock transition
• Spin-orbit coupled Fermi liquid theory of ultra-cold magnetic dipolar fermions
• Sound Propagation in Nematic Fermi Liquid
• Mott made easy
• Slater and Mott insulating states in the SU(6) Hubbard model
• Isoelectronic perturbations to $f$-$d$-electron hybridization and the enhancement of hidden order in URu${}_2$Si${}_2$
• Mott insulating phases and quantum phase transitions of interacting spin-3/2 fermionic cold atoms in optical lattices at half filling
• Crystal structure of the inversion-breaking metal Cd2Re2O7
• Floquet-Band Engineering of Shaken Bosonic Condensates
• Critical Nature of Non-Fermi Liquid in Spin 3/2 Multipolar Kondo Model
• Properties of the doped spin 3/2 Mott insulator near half filling
• Construction of $G_2$ symmetry in a Hubbard-type model