27 research outputs found
Erratum: algebraic spin liquid as the mother of many competing orders
We correct an error in our paper Phys. Rev. B 72, 104404 (2005)
[cond-mat/0502215]. We show that a particular fermion bilinear is not related
to the other ``competing orders'' of the algebraic spin liquid, and does not
possess their slowly decaying correlations. For the square lattice staggered
flux spin liquid (equivalently, d-wave RVB state), this observable corresponds
to the uniform spin chirality.Comment: 1.25 page
Topological Entanglement Entropy of Fracton Stabilizer Codes
Entanglement entropy provides a powerful characterization of two-dimensional
gapped topological phases of quantum matter, intimately tied to their
description by topological quantum field theories (TQFTs). Fracton topological
orders are three-dimensional gapped topologically ordered states of matter, but
the existence of a TQFT description for these phases remains an open question.
We show that three-dimensional fracton phases are nevertheless characterized,
at least partially, by universal structure in the entanglement entropy of their
ground state wave functions. We explicitly compute the entanglement entropy for
two archetypal fracton models --- the `X-cube model' and `Haah's code' --- and
demonstrate the existence of a topological contribution that scales linearly in
subsystem size. We show via Schrieffer-Wolff transformations that the
topological entanglement of fracton models is robust against arbitrary local
perturbations of the Hamiltonian. Finally, we argue that these results may be
extended to characterize localization-protected fracton topological order in
excited states of disordered fracton models.Comment: published versio
Odd Fracton Theories, Proximate Orders, and Parton Constructions
The Lieb-Schultz-Mattis (LSM) theorem implies that gapped phases of matter
must satisfy non-trivial conditions on their low-energy properties when a
combination of lattice translation and symmetry are imposed. We describe
a framework to characterize the action of symmetry on fractons and other
sub-dimensional fractional excitations, and use this together with the LSM
theorem to establish that X-cube fracton order can occur only at integer or
half-odd-integer filling. Using explicit parton constructions, we demonstrate
that "odd" versions of X-cube fracton order can occur in systems at
half-odd-integer filling, generalizing the notion of odd gauge theory to
the fracton setting. At half-odd-integer filling, exiting the X-cube phase by
condensing fractional quasiparticles leads to symmetry-breaking, thereby
allowing us to identify a class of conventional ordered phases proximate to
phases with fracton order. We leverage a dual description of one of these
ordered phases to show that its topological defects naturally have restricted
mobility. Condensing pairs of these defects then leads to a fracton phase,
whose excitations inherit these mobility restrictions
Synthetic gauge fields stabilize a chiral spin liquid phase
We calculate the phase diagram of the SU() Hubbard model describing
fermionic alkaline earth atoms in a square optical lattice with on-average one
atom per site, using a slave-rotor mean-field approximation. We find that the
chiral spin liquid predicted for and large interactions passes through
a fractionalized state with a spinon Fermi surface as interactions are
decreased before transitioning to a weakly interacting metal. We also show that
by adding an artificial uniform magnetic field with flux per plaquette
, the chiral spin liquid becomes the ground state for all at
large interactions, persists to weaker interactions, and its spin gap
increases, suggesting that the spin liquid physics will persist to higher
temperatures. We discuss potential methods to realize the artificial gauge
fields and detect the predicted phases
Algebraic spin liquid as the mother of many competing orders
We study the properties of a class of two-dimensional interacting critical
states -- dubbed algebraic spin liquids -- that can arise in two-dimensional
quantum magnets. A particular example that we focus on is the staggered flux
spin liquid, which plays a key role in some theories of underdoped cuprate
superconductors. We show that the low-energy theory of such states has much
higher symmetry than the underlying microscopic spin system. This symmetry has
remarkable consequences, leading in particular to the unification of a number
of seemingly unrelated competing orders. The correlations of these orders --
including, in the staggered flux state, the Neel vector and the order parameter
for the columnar and box valence-bond solid states -- all exhibit the SAME slow
power-law decay. Implications for experiments in the pseudogap regime of the
cuprates and for numerical calculations on model systems are discussed.Comment: Minor changes; final published version. 17 pages, 3 figure
Monopoles in CP(N-1) model via the state-operator correspondence
One of the earliest proposed phase transitions beyond the
Landau-Ginzburg-Wilson paradigm is the quantum critical point separating an
antiferromagnet and a valence-bond-solid on a square lattice. The low energy
description of this transition is believed to be given by the 2+1 dimensional
CP(1) model -- a theory of bosonic spinons coupled to an abelian gauge field.
Monopole defects of the gauge field play a prominent role in the physics of
this phase transition. In the present paper, we use the state-operator
correspondence of conformal field theory in conjunction with the 1/N expansion
to study monopole operators at the critical fixed point of the CP(N-1) model.
This elegant method reproduces the result for monopole scaling dimension
obtained through a direct calculation by Murthy and Sachdev. The technical
simplicity of our approach makes it the method of choice when dealing with
monopole operators in a conformal field theory.Comment: 14 pages, 1 figur