365 research outputs found
An exactly solvable quench protocol for integrable spin models
Quantum quenches in continuum field theory across critical points are known
to display different scaling behaviours in different regimes of the quench
rate. We extend these results to integrable lattice models such as the
transverse field Ising model on a one-dimensional chain and the Kitaev model on
a two-dimensional honeycomb lattice using a nonlinear quench protocol which
allows for exact analytical solutions of the dynamics. Our quench protocol
starts with a finite mass gap at early times and crosses a critical point or a
critical region, and we study the behaviour of one point functions of the
quenched operator at the critical point or in the critical region as a function
of the quench rate. For quench rates slow compared to the initial mass gap, we
find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to
the mass gap, but slow compared to the inverse lattice spacing, we find scaling
behaviour similar to smooth fast continuum quenches. For quench rates of the
same order of the lattice scale, the one point function saturates as a function
of the rate, approaching the results of an abrupt quench. The presence of an
extended critical surface in the Kitaev model leads to a variety of scaling
exponents depending on the starting point and on the time where the operator is
measured. We discuss the role of the amplitude of the quench in determining the
extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the
saturation.Comment: 54 pages, 13 figures; v2: added analytic argument for Kitaev mode
Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two
We find classes of driven conformal field theories (CFT) in d+1 dimensions
with d > 1, whose quench and floquet dynamics can be computed exactly. The
setup is suitable for studying periodic drives, consisting of square pulse
protocols for which Hamiltonian evolution takes place with different
deformations of the original CFT Hamiltonian in successive time intervals.
These deformations are realized by specific combinations of conformal
generators with a deformation parameter ; the )
Hamiltonians can be unitarily related to the standard (L\"uscher-Mack) CFT
Hamiltonians. The resulting time evolution can be then calculated by performing
appropriate conformal transformations. For d <= 3 we show that the
transformations can be easily obtained in a quaternion formalism; we use this
formalism to obtain exact expressions for the fidelity, unequal-time
correlator, and the energy density for the driven system for d = 3. Our results
for a single square pulse drive cycle reveal qualitatively different behaviors
depending on the value of , with exponential decays characteristic of
heating for , oscillations for and power law decays for
. When the Hamiltonians in one cycle involve generators of a single
SL(2, R) subalgebra we find fixed points or fixed surfaces of the corresponding
transformations. Successive cycles lead to either convergence to one of the
fixed points, or oscillations, depending on the conjugacy class. This indicates
that the system can be in different dynamical phases as we vary the parameters
of the drive protocol. We also point out that our results are expected to hold
for a broader class of QFTs that possesses an SL(2,C) symmetry with fields that
transform as quasi-primaries under this. As an example, we briefly comment on
celestial CFTs in this context.Comment: 32 pages, 10 figure
Non-equilibrium dynamics of Bosonic Mott insulators in an electric field
We study the non-equilibrium dynamics of one-dimensional Mott insulating
bosons in the presence of a tunable effective electric field E which takes the
system across a quantum critical point (QCP) separating a disordered and a
translation symmetry broken ordered phase. We provide an exact numerical
computation of the residual energy Q, the log-fidelity F, the excess defect
density D, and the order parameter correlation function for a linear-in-time
variation of E with a rate v. We discuss the temporal and spatial variation of
these quantities for a range of v and for finite system sizes as relevant to
realistic experimental setups [J. Simon et al., Nature 472, 307 (2011)]. We
show that in finite-sized systems Q, F, and D obey Kibble-Zurek scaling, and
suggest further experiments within this setup to test our theory.Comment: 4+epsilon pages, 3 figure
Competing orders II: the doped quantum dimer model
We study the phases of doped spin S=1/2 quantum antiferromagnets on the
square lattice, as they evolve from paramagnetic Mott insulators with valence
bond solid (VBS) order at zero doping, to superconductors at moderate doping.
The interplay between density wave/VBS order and superconductivity is
efficiently described by the quantum dimer model, which acts as an effective
theory for the total spin S=0 sector. We extend the dimer model to include
fermionic S=1/2 excitations, and show that its mean-field, static gauge field
saddle points have projective symmetries (PSGs) similar to those of `slave'
particle U(1) and SU(2) gauge theories. We account for the non-perturbative
effects of gauge fluctuations by a duality mapping of the S=0 dimer model. The
dual theory of vortices has a PSG identical to that found in a previous paper
(L. Balents et al., cond-mat/0408329) by a duality analysis of bosons on the
square lattice. The previous theory therefore also describes fluctuations
across superconducting, supersolid and Mott insulating phases of the present
electronic model. Finally, with the aim of describing neutron scattering
experiments, we present a phenomenological model for collective S=1 excitations
and their coupling to superflow and density wave fluctuations.Comment: 22 pages, 10 figures; part I is cond-mat/0408329; (v2) changed title
and added clarification
Putting competing orders in their place near the Mott transition
We describe the localization transition of superfluids on two-dimensional
lattices into commensurate Mott insulators with average particle density p/q
(p, q relatively prime integers) per lattice site. For bosons on the square
lattice, we argue that the superfluid has at least q degenerate species of
vortices which transform under a projective representation of the square
lattice space group (a PSG). The formation of a single vortex condensate
produces the Mott insulator, which is required by the PSG to have density wave
order at wavelengths of q/n lattice sites (n integer) along the principle axes;
such a second-order transition is forbidden in the Landau-Ginzburg-Wilson
framework. We also discuss the superfluid-insulator transition in the direct
boson representation, and find that an interpretation of the quantum
criticality in terms of deconfined fractionalized bosons is only permitted at
special values of q for which a permutative representation of the PSG exists.
We argue (and demonstrate in detail in a companion paper: L. Balents et al.,
cond-mat/0409470) that our results apply essentially unchanged to electronic
systems with short-range pairing, with the PSG determined by the particle
density of Cooper pairs. We also describe the effect of static impurities in
the superfluid: the impurities locally break the degeneracy between the q
vortex species, and this induces density wave order near each vortex. We
suggest that such a theory offers an appealing rationale for the local density
of states modulations observed by Hoffman et al. (cond-mat/0201348) in STM
studies of the vortex lattice of BSCCO, and allows a unified description of the
nucleation of density wave order in zero and finite magnetic fields. We note
signatures of our theory that may be tested by future STM experiments.Comment: 35 pages, 16 figures; (v2) part II is cond-mat/0409470; (v3) added
new appendix and clarifying remarks; (v4) corrected typo
Commensurate lock-in and incommensurate supersolid phases of hardcore bosons on anisotropic triangular lattices
We investigate the interplay between commensurate lock-in and incommensurate
supersolid phases of the hardcore bosons at half-filling with anisotropic
nearest-neighbor hopping and repulsive interactions on triangular lattice. We
use numerical quantum and variational Monte Carlo as well as analytical
Schwinger boson mean-field analysis to establish the ground states and phase
diagram. It is shown that, for finite size systems, there exist a series of
jumps between different supersolid phases as the anisotropy parameter is
changed. The density ordering wavevectors are locked to commensurate values and
jump between adjacent supersolids. In the thermodynamic limit, however, the
magnitude of these jumps vanishes leading to a continuous set of novel
incommensurate supersoild phases.Comment: 5 pages, 5 figures, added new results, changed title and conclusio
Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N approach
We study the time evolution of the mass gap of the O(N) non-linear sigma
model in 2+1 dimensions due to a time-dependent coupling in the large-
limit. Using the Schwinger-Keldysh approach, we derive a set of equations at
large which determine the time dependent gap in terms of the coupling.
These equations lead to a criterion for the breakdown of adiabaticity for slow
variation of the coupling leading to a Kibble-Zurek scaling law. We describe a
self-consistent numerical procedure to solve these large- equations and
provide explicit numerical solutions for a coupling which starts deep in the
gapped phase at early times and approaches the zero temperature equilibrium
critical point in a linear fashion. We demonstrate that for such a
protocol there is a value of the coupling where the gap
function vanishes, possibly indicating a dynamical instability. We study the
dependence of on both the rate of change of the coupling and
the initial temperature. We also verify, by studying the evolution of the mass
gap subsequent to a sudden change in , that the model does not display
thermalization within a finite time interval and discuss the implications
of this observation for its conjectured gravitational dual as a higher spin
theory in .Comment: 22 pages, 9 figures. Typos corrected, references rearranged and
added.v3 : sections rearranged, abstract modified, comment about Kibble-Zurek
scaling correcte
- …