We consider the
O(3) nonlinear sigma model with the $\ensuremath{\theta}$ term and its linear counterpart in 1+1D. The model has discrete time-reflection and space-reflection symmetries at any $\ensuremath{\theta}$, and enjoys the periodicity in $\ensuremath{\theta}\ensuremath{\rightarrow}\ensuremath{\theta}+2\ensuremath{\pi}$. At $\ensuremath{\theta}=0,\ensuremath{\pi}$ it also has a charge-conjugation
C symmetry. Gauging the discrete space-time reflection symmetries is interpreted as putting the theory on the nonorientable
RP2 manifold, after which the $2\ensuremath{\pi}$ periodicity of $\ensuremath{\theta}$ and the
C symmetry at $\ensuremath{\theta}=\ensuremath{\pi}$ are lost. We interpret this observation as a mixed 't Hooft anomaly among charge-conjugation
C, parity
P, and time-reversal
T symmetries when $\ensuremath{\theta}=\ensuremath{\pi}$. Anomaly matching implies that in this case the ground state cannot be trivially gapped, as long as
C,P, and
T are all good symmetries of the theory. We make several consistency checks with various semiclassical regimes, and with the exactly solvable XYZ model. We interpret this anomaly as an anomaly of the corresponding spin-half chains with translational symmetry, parity, and time reversal [but not involving the SO(3)-spin symmetry], requiring that the ground state is never trivially gapped, even if SO(3) spin symmetry is explicitly and completely broken. We also consider generalizations to $\mathbb{C}{P}^{N\ensuremath{-}1}$ models and show that the $C\text{\ensuremath{-}}P\text{\ensuremath{-}}T$ anomaly exists for even
N.
Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductor--anyon superconductor. Such an exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in a realistic system where time-reversal symmetry is breaking (T breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneous T breaking. We find that our model has two topological degenerate ground states, which exhibit nonvanishing scalar chirality order and are protected by finite excitation gap. Furthermore, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest-neighbor kagome Heisenberg model.
Novel critical phenomena beyond the Landau-Ginzburg-Wilson paradigm have been long sought after. Among many candidate scenarios, the deconfined quantum critical point (DQCP) constitutes the most fascinating one, and its lattice model realization has been debated over the past two decades. Here we apply the spherical Landau level regularization upon the exact (2+1)D SO(5) nonlinear sigma model with a topological term to study the potential DQCP therein. We perform a density matrix renormalization group (DMRG) simulation with SU(2)_{spin}×U(1)_{charge}×U(1)_{angular-momentum} symmetries explicitly implemented. Using crossing point analysis for the critical properties of the DMRG data, accompanied by quantum Monte Carlo simulations, we accurately obtain the comprehensive phase diagram of the model and find various novel quantum phases, including Néel, ferromagnet (FM), valence bond solid (VBS), valley polarized (VP) states and a gapless quantum disordered phase occupying an extended area of the phase diagram. The VBS-disorder and Néel-disorder transitions are continuous with non-Wilson-Fisher exponents. Our results show the VBS and Néel states are separated by either a weakly first-order transition or the disordered region with a multicritical point in between, thus opening up more interesting questions on the two-decade long debate on the nature of the DQCP.
We study mixed quantum spin chains consisting of two kinds of spins with magnitudes
sa and
sb. The spins are arrayed as ${s}_{a}\ensuremath{-}{s}_{a}\ensuremath{-}{s}_{b}\ensuremath{-}{s}_{b}$ in a unit cell and the exchange couplings are accordingly periodic with period 4. The spin Hamiltonian is mapped onto a nonlinear $\ensuremath{\sigma}$ model based on the general formula for periodic inhomogeneous spin chains. The gapless condition given by the nonlinear $\ensuremath{\sigma}$ model determines boundaries between disordered phases in the space of the exchange parameters. The phase diagram has a rich phase structure characterized by the values of
sa and
sb. We explain all phases in the singlet-cluster-solid picture which is an extension of the valence-bond-solid picture.
We investigate disordered phases realized in one-dimensional quantum spin systems.We revisit an effective field theory proposed by Schulz [Phys.Rev. B 34, 6372 (1986)], which encapsulates several essential properties in low energy, from the point of view of symmetry.Although this effective theory was originally derived by perturbation theory, we find that it is fully consistent with the symmetry of the Hamiltonian and thus uniquely identified in the non-perturbative sense.This theory explains many possible phase transitions known to occur among valence-bond-solid phases, which are typical disordered phases in one-dimensional spin systems.Furthermore, this theory indicates that the phase transitions only occur under one of four symmetries: time reversal, bond-centered inversion, dihedral group of spin rotations, and site-centered inversion combined with a spin rotation.Surprisingly, the first three symmetries are consistent with those protecting the Haldane phase in spin-1 chains, which have already been found by a completely different approach using the matrix-product state (MPS).On the other hand, the last one is not known so far.To understand it, we explicitly construct a microscopic model that has two distinct disordered phases protected by the combined inversion symmetry.We examine this model and confirm the existence of those disordered phases by perturbation theory and numerical simulations.For completeness, we further give a more rigorous proof of their existence, based on the non-translation-invariant MPS.We also propose an extension of the Lieb-Schultz-Mattis theorem for the absence of a unique gapped ground state in half-odd-integer spin systems with site-centered inversion symmetry.
We study the ground-state density profile of a spin-orbit-coupled
f=2 spinor condensate in a quasi-one-dimensional trap. The Hamiltonian of the system is invariant under time reversal but not under parity. We identify different parity- and time-reversal symmetry-breaking states. The time-reversal symmetry breaking is possible for degenerate states. A phase separation among densities of different components is possible in the domain of time-reversal symmetry breaking. Different types of parity- and time-reversal symmetry-breaking states are predicted analytically and studied numerically. We employ numerical and approximate analytic solutions of a mean-field model in this investigation to illustrate our findings.