20 research outputs found
Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries
We prove two Lieb-Schultz-Mattis type theorems that apply to any translationally invariant and local fermionic d-dimensional lattice Hamiltonians for which fermion-number conservation is broken down to the conservation of fermion parity. We show that when the internal symmetry group Gf is realized locally (in a repeat unit cell of the lattice) by a nontrivial projective representation, then the ground state cannot be simultaneously nondegenerate, symmetric (with respect to lattice translations and Gf), and gapped. We also show that when the repeat unit cell hosts an odd number of Majorana degrees of freedom and the cardinality of the lattice is even, then the ground state cannot be simultaneously nondegenerate, gapped, and translation symmetric
Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
Lieb-Schultz-Mattis (LSM) theorems impose non-perturbative constraints on the
zero-temperature phase diagrams of quantum lattice Hamiltonians (always assumed
to be local in this paper). LSM theorems have recently been interpreted as the
lattice counterparts to mixed 't Hooft anomalies in quantum field theories that
arise from a combination of crystalline and global internal symmetry groups.
Accordingly, LSM theorems have been reinterpreted as LSM anomalies. In this
work, we provide a systematic diagnostic for LSM anomalies in one spatial
dimension. We show that gauging subgroups of the global internal symmetry group
of a quantum lattice model obeying an LSM anomaly delivers a dual quantum
lattice Hamiltonian such that its internal and crystalline symmetries mix
non-trivially through a group extension. This mixing of crystalline and
internal symmetries after gauging is a direct consequence of the LSM anomaly,
i.e., it can be used as a diagnostic of an LSM anomaly. We exemplify this
procedure for a quantum spin-1/2 chain obeying an LSM anomaly resulting from
combining a global internal
symmetry with translation or reflection symmetry. We establish a triality of
models by gauging a
symmetry in two ways, one of which amounts to performing a Kramers-Wannier
duality, while the other implements a Jordan-Wigner duality. We discuss the
mapping of the phase diagram of the quantum spin-1/2 chains under such a
triality. We show that the deconfined quantum critical transitions between Neel
and dimer orders are mapped to either topological or conventional
Landau-Ginzburg transitions.Comment: 84 pages, 6 figure
Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
We investigate the gauging of higher-form finite Abelian symmetries and their
sub-groups in quantum spin models in spatial dimensions and 3. Doing so,
we naturally uncover gauged models with dual higher-group symmetries and
potential mixed 't Hooft anomalies. We demonstrate that the mixed anomalies
manifest as the symmetry fractionalization of higher-form symmetries
participating in the mixed anomaly. Gauging is realized as an isomorphism or
duality between the bond algebras that generate the space of quantum spin
models with the dual generalized symmetry structures. We explore the mapping of
gapped phases under such gauging related dualities for 0-form and 1-form
symmetries in spatial dimension and 3. In , these include several
non-trivial dualities between short-range entangled gapped phases with 0-form
symmetries and 0-form symmetry enriched Higgs and (twisted) deconfined phases
of the gauged theory with possible symmetry fractionalizations. Such dualities
also imply strong constraints on several unconventional, i.e., deconfined or
topological transitions. In , among others, we find, dualities between
topological orders via gauging of 1-form symmetries. Hamiltonians self-dual
under gauging of 1-form symmetries host emergent non-invertible symmetries,
realizing higher-categorical generalizations of the Tambara-Yamagami fusion
category.Comment: 90 pages, 19 figure
Single monkey-saddle singularity of a Fermi surface and its instabilities
Fermi surfaces can undergo sharp transitions under smooth changes of parameters. Such transitions can have a topological character, as is the case when a higher-order singularity, one that requires cubic or higher-order terms to describe the electronic dispersion near the singularity, develops at the transition. When time-reversal and inversion symmetries are present, odd singularities can only appear in pairs within the Brillouin zone. In this case, the combination of the enhanced density of states that accompanies these singularities and the nesting between the pairs of singularities leads to interaction-driven instabilities. We present examples of single n=3 (monkey-saddle) singularities when time-reversal and inversion symmetries are broken. We then turn to the question of what instabilities are possible when the singularities are isolated. For spinful electrons, we find that the inclusion of repulsive interactions destroys any isolated monkey-saddle singularity present in the noninteracting spectrum by developing Stoner or Lifshitz instabilities. In contrast, for spinless electrons and at the mean-field level, we show that an isolated monkey-saddle singularity can be stabilized in the presence of short-range repulsive interactions