Loop models on random maps via nested loops: case of domain symmetry breaking and application to the Potts model

We use the nested loop approach to investigate loop models on random planar maps where the domains delimited by the loops are given two alternating colors, which can be assigned different local weights, hence allowing for an explicit Z_2 domain symmetry breaking. Each loop receives a non local weight n, as well as a local bending energy which controls loop turns. By a standard cluster construction that we review, the Q = n^2 Potts model on general random maps is mapped to a particular instance of this problem with domain-non-symmetric weights. We derive in full generality a set of coupled functional relations for a pair of generating series which encode the enumeration of loop configurations on maps with a boundary of a given color, and solve it by extending well-known complex analytic techniques. In the case where loops are fully-packed, we analyze in details the phase diagram of the model and derive exact equations for the position of its non-generic critical points. In particular, we underline that the critical Potts model on general random maps is not self-dual whenever Q \neq 1. In a model with domain-symmetric weights, we also show the possibility of a spontaneous domain symmetry breaking driven by the bending energy.Comment: 44 pages, 13 figure

Entanglement spectra of critical and near-critical systems in one dimension

The entanglement spectrum of a pure state of a bipartite system is the full set of eigenvalues of the reduced density matrix obtained from tracing out one part. Such spectra are known in several cases to contain important information beyond that in the entanglement entropy. This paper studies the entanglement spectrum for a variety of critical and near-critical quantum lattice models in one dimension, chiefly by the iTEBD numerical method, which enables both integrable and non-integrable models to be studied. We find that the distribution of eigenvalues in the entanglement spectra agrees with an approximate result derived by Calabrese and Lefevre to an accuracy of a few percent for all models studied. This result applies whether the correlation length is intrinsic or generated by the finite matrix size accessible in iTEBD. For the transverse Ising model, the known exact results for the entanglement spectrum are used to confirm the validity of the iTEBD approach. For more general models, no exact result is available but the iTEBD results directly test the hypothesis that all moments of the reduced density matrix are determined by a single parameter.Comment: 6 pages, 5 figure

An Intersecting Loop Model as a Solvable Super Spin Chain

In this paper we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical regime, we conjecture that the central charge is $c=q-1$ for $q$ integer $< 2$. Low-lying excitations are examined, supporting a superdiffusive behavior for $q=1$. We argue that these systems are interesting examples of integrable lattice models realizing $c \leq 0$ conformal field theories.Comment: latex file, 7 page

Boundary and Bulk Phase Transitions in the Two Dimensional Q > 4 State Potts Model

The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q \to \infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point.Comment: 11 pages, RevTeX, 6 PostScript figures included. Manuscript substantially extended, details on the analytical and numerical calculations added. To appear in Phys. Rev.

Two-dimensional periodic frustrated Ising models in a transverse field

We investigate the interplay of classical degeneracy and quantum dynamics in a range of periodic frustrated transverse field Ising systems at zero temperature. We find that such dynamics can lead to unusual ordered phases and phase transitions, or to a quantum spin liquid (cooperative paramagnetic) phase as in the triangular and kagome lattice antiferromagnets, respectively. For the latter, we further predict passage to a bond-ordered phase followed by a critical phase as the field is tilted. These systems also provide exact realizations of quantum dimer models introduced in studies of high temperature superconductivity.Comment: Revised introduction; numerical error in hexagonal section correcte

Supersymmetric quantum mechanics with nonlocal potentials

We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe that both our model Hamiltonian and its supersymmetric partner may have normalizable zero-energy ground states, in contrast to local models with nonperiodic or periodic potentials.Comment: 4 pages, REVTeX, Minor revisions for clarificatio

Charge 4e4e superconductivity from pair density wave order in certain high temperature superconductors

A number of spectacular experimental anomalies\cite{li-2007,fujita-2005} have recently been discovered in certain cuprates, notably {\LBCO} and {\LNSCO}, which exhibit unidirectional spin and charge order (known as ``stripe order''). We have recently proposed to interpret these observations as evidence for a novel ``striped superconducting'' state, in which the superconducting order parameter is modulated in space, such that its average is precisely zero. Here, we show that thermal melting of the striped superconducting state can lead to a number of unusual phases, of which the most novel is a charge $4e$ superconducting state, with a corresponding fractional flux quantum $hc/4e$. These are never-before observed states of matter, and ones, moreover, that cannot arise from the conventional Bardeen-Cooper-Schrieffer (BCS) mechanism. Thus, direct confirmation of their existence, even in a small subset of the cuprates, could have much broader implications for our understanding of high temperature superconductivity. We propose experiments to observe fractional flux quantization, which thereby could confirm the existence of these states.Comment: 5 pages, 2 figures; new version in Nature Physics format with a discussion of the effective Josephson coupling J2 and minor changes. Mildly edited abstract. v3: corrected versio

Differential expression of DNA topoisomerase II alpha and -beta in P-gp and MRP-negative VM26, mAMSA and mitoxantrone-resistant sublines of the human SCLC cell line GLC4.

Sublines of the human small-cell lung carcinoma (SCLC) cell line GLC4 with acquired resistance to teniposide, amsacrine and mitoxantrone (GLC4/VM20x, GLC4/AM3x and GLC4/MIT60x, respectively) were derived to study the contribution of DNA topoisomerase II alpha and -beta (TopoII alpha and -beta) to resistance for TopoII-targeting drugs. The cell lines did not overexpress P-glycoprotein or the multidrug resistance-associated protein but were cross-resistant to other TopoII drugs. GLC4/VM20x showed a major decrease in TopoII alpha protein (54%; for all assays presented in this paper the GLC4 level was defined to be 100%) without reduction in TopoII beta protein; GLC4/AM3x showed only a major decrease in TopoII beta protein (to 18%) and not in TopoII alpha. In GLC4/MIT60x, the TopoII alpha and -beta protein levels were both decreased (TopoII alpha to 31%; TopoII beta protein was undetectable). The decrease in TopoII alpha protein in GLC4/VM20x and GLC4/MIT60x, was mediated by decreased TopoII alpha mRNA levels. Loss of TopoII alpha gene copies contributed to the mRNA decrease in these cell lines. Only in the GLC4/MIT60x cell line was an accumulation defect observed for the drug against which the cell line was made resistant. In conclusion, TopoII alpha and -beta levels were decreased differentially in the resistant cell lines, suggesting that resistance to these drugs may be mediated by a decrease in a specific isozyme

Continuous phase transition in a spin-glass model without time-reversal symmetry

We investigate the phase transition in a strongly disordered short-range three-spin interaction model characterized by the absence of time reversal symmetry in the Hamiltonian. In the mean-field limit the model is well described by the Adam-Gibbs-DiMarzio scenario for the glass transition; however in the short-range case this picture turns out to be modified. The model presents a finite temperature continuous phase transition characterized by a divergent spin-glass susceptibility and a negative specific heat exponent. We expect the nature of the transition in this 3-spin model to be the same as the transition in the Edwards-Anderson model in a magnetic field, with the advantage that the strong crossover effects present in the latter case are absent.Comment: 19 pages, Latex, 16 ps figure

On harmonic measure of critical curves

Fractal geometry of critical curves appearing in 2D critical systems is characterized by their harmonic measure. For systems described by conformal field theories with central charge $c\leqslant 1$, scaling exponents of harmonic measure have been computed by B. Duplantier [Phys. Rev. Lett. {\bf 84}, 1363 (2000)] by relating the problem to boundary two-dimensional gravity. We present a simple argument that allows us to connect harmonic measure of critical curves to operators obtained by fusion of primary fields, and compute characteristics of fractal geometry by means of regular methods of conformal field theory. The method is not limited to theories with $c\leqslant 1$.Comment: Some more correction