210 research outputs found
Quench dynamics across quantum critical points
We study the quantum dynamics of a number of model systems as their coupling
constants are changed rapidly across a quantum critical point. The primary
motivation is provided by the recent experiments of Greiner et al. (Nature 415,
39 (2002)) who studied the response of a Mott insulator of ultracold atoms in
an optical lattice to a strong potential gradient. In a previous work
(cond-mat/0205169), it had been argued that the resonant response observed at a
critical potential gradient could be understood by proximity to an Ising
quantum critical point describing the onset of density wave order. Here we
obtain numerical results on the evolution of the density wave order as the
potential gradient is scanned across the quantum critical point. This is
supplemented by studies of the integrable quantum Ising spin chain in a
transverse field, where we obtain exact results for the evolution of the Ising
order correlations under a time-dependent transverse field. We also study the
evolution of transverse superfluid order in the three dimensional case. In all
cases, the order parameter is best enhanced in the vicinity of the quantum
critical point.Comment: 10 pages, 6 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
Mott insulators in strong electric fields
Recent experiments on ultracold atomic gases in an optical lattice potential
have produced a Mott insulating state of Rb atoms. This state is stable to a
small applied potential gradient (an `electric' field), but a resonant response
was observed when the potential energy drop per lattice spacing (E), was close
to the repulsive interaction energy (U) between two atoms in the same lattice
potential well. We identify all states which are resonantly coupled to the Mott
insulator for E close to U via an infinitesimal tunneling amplitude between
neighboring potential wells. The strong correlation between these states is
described by an effective Hamiltonian for the resonant subspace. This
Hamiltonian exhibits quantum phase transitions associated with an Ising density
wave order, and with the appearance of superfluidity in the directions
transverse to the electric field. We suggest that the observed resonant
response is related to these transitions, and propose experiments to directly
detect the order parameters. The generalizations to electric fields applied in
different directions, and to a variety of lattices, should allow study of
numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference
Competing density-wave orders in a one-dimensional hard-boson model
We describe the zero-temperature phase diagram of a model of bosons,
occupying sites of a linear chain, which obey a hard-exclusion constraint: any
two nearest-neighbor sites may have at most one boson. A special case of our
model was recently proposed as a description of a ``tilted'' Mott insulator of
atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to
generate the transfer matrix of Baxter's hard-square model. Aided by exact
solutions of a number of special cases, and by numerical studies, we obtain a
phase diagram containing states with long-range density-wave order with period
2 and period 3, and also a floating incommensurate phase. Critical theories for
the various quantum phase transitions are presented. As a byproduct, we show
how to compute the Luttinger parameter in integrable theories with
hard-exclusion constraints.Comment: 16 page
Non-Fermi liquid behavior from two-dimensional antiferromagnetic fluctuations: a renormalization-group and large-N analysis
We analyze the Hertz-Moriya-Millis theory of an antiferromagnetic quantum
critical point, in the marginal case of two dimensions (d=2,z=2). Up to
next-to-leading order in the number of components (N) of the field, we find
that logarithmic corrections do not lead to an enhancement of the Landau
damping. This is in agreement with a renormalization-group analysis, for
arbitrary N. Hence, the logarithmic effects are unable to account for the
behavior reportedly observed in inelastic neutron scattering experiments on
CeCu_{6-x}Au_x. We also examine the extended dynamical mean-field treatment
(local approximation) of this theory, and find that only subdominant
corrections to the Landau damping are obtained within this approximation, in
contrast to recent claims.Comment: 15 pages, 8 figure
Quantum field theory of metallic spin glasses
We introduce an effective field theory for the vicinity of a zero temperature
quantum transition between a metallic spin glass (``spin density glass'') and a
metallic quantum paramagnet. Following a mean field analysis, we perform a
perturbative renormalization-group study and find that the critical properties
are dominated by static disorder-induced fluctuations, and that dynamic
quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point
is stable for a finite range of couplings for spatial dimensionality ,
but disorder effects always lead to runaway flows to strong coupling for . Scaling hypotheses for a {\em static\/} strong-coupling critical field
theory are proposed. The non-linear susceptibility has an anomalously weak
singularity at such a critical point. Although motivated by a perturbative
study of metallic spin glasses, the scaling hypotheses are more general, and
could apply to other quantum spin glass to paramagnet transitions.Comment: 16 pages, REVTEX 3.0, 2 postscript figures; version contains
reference to related work in cond-mat/950412
Theory of finite temperature crossovers near quantum critical points close to, or above, their upper-critical dimension
A systematic method for the computation of finite temperature () crossover
functions near quantum critical points close to, or above, their upper-critical
dimension is devised. We describe the physics of the various regions in the
and critical tuning parameter () plane. The quantum critical point is at
, , and in many cases there is a line of finite temperature
transitions at , with . For the relativistic,
-component continuum quantum field theory (which describes lattice
quantum rotor () and transverse field Ising () models) the upper
critical dimension is , and for , is the control
parameter over the entire phase diagram. In the region , we obtain an expansion for coupling constants which then are
input as arguments of known {\em classical, tricritical,} crossover functions.
In the high region of the continuum theory, an expansion in integer powers
of , modulo powers of , holds for all
thermodynamic observables, static correlators, and dynamic properties at all
Matsubara frequencies; for the imaginary part of correlators at real
frequencies (), the perturbative expansion describes
quantum relaxation at or larger, but fails for or smaller. An important principle,
underlying the whole calculation, is the analyticity of all observables as
functions of at , for ; indeed, analytic continuation in is
used to obtain results in a portion of the phase diagram. Our method also
applies to a large class of other quantum critical points and their associated
continuum quantum field theories.Comment: 36 pages, 4 eps figure
Spin orthogonality catastrophe in two-dimensional antiferromagnets and superconductors
We compute the spectral function of a spin S hole injected into a
two-dimensional antiferromagnet or superconductor in the vicinity of a magnetic
quantum critical point. We show that, near van Hove singularities, the problem
maps onto that of a static vacancy carrying excess spin S. The hole creation
operator is characterized by a new boundary anomalous dimension and a vanishing
quasiparticle residue at the critical point. We discuss possible relevance to
photoemission spectra of cuprate superconductors near the anti-nodal points.Comment: (v1) 4 pages, 2 figures; field theory afficionados - see also
cond-mat/0011233; (v2) added figure of Monte Carlo data; (v3) corrected typo
- …