725 research outputs found
Phase transitions in one dimension and less
Phase transitions can occur in one-dimensional classical statistical
mechanics at non-zero temperature when the number of components N of the spin
is infinite. We show how to solve such magnets in one dimension for any N, and
how the phase transition develops at N = infinity. We discuss SU(N) and Sp(N)
magnets, where the transition is second-order. In the new high-temperature
phase, the correlation length is zero. We also show that for the SU(N) magnet
on exactly three sites with periodic boundary conditions, the transition
becomes first order.Comment: 16 pages, 1 figur
Quantum criticality in a generalized Dicke model
We employ a generalized Dicke model to study theoretically the quantum
criticality of an extended two-level atomic ensemble interacting with a
single-mode quantized light field. Effective Hamiltonians are derived and
diagonalized to investigate numerically their eigenfrequencies for different
quantum phases in the system. Based on the analysis of the eigenfrequencies, an
intriguing quantum-phase transition from a normal phase to a superradiant phase
is revealed clearly, which is quite different from that observed with a
standard Dicke model.Comment: 6 pages, 3 figure
Frustration and glassiness in spin models with cavity-mediated interactions
We show that the effective spin-spin interaction between three-level atoms
confined in a multimode optical cavity is long-ranged and sign-changing, like
the RKKY interaction; therefore, ensembles of such atoms subject to frozen-in
positional randomness can realize spin systems having disordered and frustrated
interactions. We argue that, whenever the atoms couple to sufficiently many
cavity modes, the cavity-mediated interactions give rise to a spin glass. In
addition, we show that the quantum dynamics of cavity-confined spin systems is
that of a Bose-Hubbard model with strongly disordered hopping but no on-site
disorder; this model exhibits a random-singlet glass phase, absent in
conventional optical-lattice realizations. We briefly discuss experimental
signatures of the realizable phases.Comment: 5 pages, 2 figure
Polarization transitions in interacting ring 1D arrays
Periodic nanostructures can display the dynamics of arrays of atoms while
enabling the tuning of interactions in ways not normally possible in Nature. We
examine one dimensional arrays of a ``synthetic atom,'' a one dimensional ring
with a nearest neighbor Coulomb interaction. We consider the classical limit
first, finding that the singly charged rings possess antiferroelectric order at
low temperatures when the charge is discrete, but that they do not order when
the charge is treated as a continuous classical fluid. In the quantum limit
Monte Carlo simulation suggests that the system undergoes a quantum phase
transition as the interaction strength is increased. This is supported by
mapping the system to the 1D transverse field Ising model. Finally we examine
the effect of magnetic fields. We find that a magnetic field can alter the
electrostatic phase transition producing a ferroelectric groundstate, solely
through its effect of shifting the eigenenergies of the quantum problem.Comment: 12 pages in two column format, 18 figure
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
Semi-classical Analysis of Spin Systems near Critical Energies
The spectral properties of Hamiltonians are studied for energies near
the critical classical energy for which the corresponding
classical dynamics presents hyperbolic points (HP). A general method leading to
an algebraic relation for eigenvalues in the vicinity of is
obtained in the thermodynamic limit, when the semi-classical parameter
goes to zero (where is the total spin of the system).
Two applications of this method are given and compared with numerics. Matrix
elements of observables, computed between states with energy near ,
are also computed and shown to be in agreement with the numerical results.Comment: 3 figure
Fidelity and quantum phase transitions
It is shown that the fidelity, a basic notion of quantum information science,
may be used to characterize quantum phase transitions, regardless of what type
of internal order is present in quantum many-body states. If the fidelity of
two given states vanishes, then there are two cases: (1) they are in the same
phase if the distinguishability results from irrelevant local information; or
(2) they are in different phases if the distinguishability results from
relevant long-distance information. The different effects of irrelevant and
relevant information are quantified, which allows us to identify unstable and
stable fixed points (in the sense of renormalization group theory). A physical
implication of our results is the occurrence of the orthogonality catastrophe
near the transition points.Comment: 5 pages, 2 figure
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Transition from the Z2 spin liquid to antiferromagnetic order: Spectrum on the torus
We describe the finite-size spectrum in the vicinity of the quantum critical point between a Z2 spin liquid and a coplanar antiferromagnet on the torus. We obtain the universal evolution of all low-lying states in an antiferromagnet with global SU(2) spin rotation symmetry, as it moves from the 4-fold topological degeneracy in a gapped Z2 spin liquid to the Anderson “tower-of-states” in the ordered antiferromagnet. Due to the existence of nontrivial order on either side of this transition, this critical point cannot be described in a conventional Landau-Ginzburg-Wilson framework. Instead it is described by a theory involving fractionalized degrees of freedom known as the O(4)∗ model, whose spectrum is altered in a significant way by its proximity to a topologically ordered phase. We compute the spectrum by relating it to the spectrum of the O(4) Wilson-Fisher fixed point on the torus, modified with a selection rule on the states, and with nontrivial boundary conditions corresponding to topological sectors in the spin liquid. The spectrum of the critical O(2N) model is calculated directly at N = ∞, which then allows a reconstruction of the full spectrum of the O(2N)∗ model at leading order in 1/N. This spectrum is a unique characteristic of the vicinity of a fractionalized quantum critical point, as well as a universal signature of the existence of proximate Z2 topological and antiferromagnetically-ordered phases, and can be compared with numerical computations on quantum antiferromagnets on two dimensional lattices.Physic
Quantum replica approach to the under-screened Kondo model
We extend the Schwinger boson large N treatment of the underscreened Kondo
model in a way that correctly captures the finite elastic phase shift in the
singular Fermi liquid. The new feature of the approach, is the introduction of
a flavor quantum number with K possible values, associated with the Schwinger
boson representation. The large N limit is taken maintaining the ratio k=K/N
fixed. This approach differs from previous approaches, in that we do not
explicitly enforce a constraint on the spin representation of the Schwinger
bosons. Instead, the energetics of the Kondo model cause the bosonic degrees of
freedom to ``self assemble'' into a ground-state in which the spins of K bosons
and N-K conduction electrons are antisymmetrically arranged into a Kondo
singlet. With this device, the large N limit can be taken, in such a way that a
fraction K/N of the Abrikosov Suhl resonance is immersed inside the Fermi sea.
We show how this method can be used to model the full energy dependence of the
singular Abrikosov Suhl resonance in the underscreened Kondo model and the
field-dependent magnetization.Comment: Revised draft, with plots explicitly showing logarithmic scaling of
inverse coupling constant. Small corrections prior to submission to journa
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