arXiv subjects

M. B. Hastings

Publications and source records attributed to M. B. Hastings.

At least 109 records · Page 6Linked to original sources

arXiv2002

Quantum Dynamics in Non-equilibrium Strongly Correlated Environments

We consider a quantum point contact between two Luttinger liquids coupled to a mechanical system (oscillator). For non-vanishing bias, we find an effective oscillator temperature that depends on the Luttinger parameter. A generalized fluctuation-dissipation relation connects the decoherence and dissipation of the oscillator to the current-voltage characteristics of the device. Via a spectral representation, this result is generalized to arbitrary leads in a weak tunneling regime.

cond-mat.str-el↗

arXiv2001

Entropic Tightening of Vibrated Chains

We investigate experimentally the distribution of configurations of a ring with an elementary topological constraint, a ``figure-8'' twist. Using vibrated granular chains, which permit controlled preparation and direct observation of such a constraint, we show that configurations where one of the loops is tight and the second is large are strongly preferred. This agrees with recent predictions for equilibrium properties of topologically-constrained polymers. However, the dynamics of the tightening process weakly violate detailed balance, a signature of the nonequilibrium nature of this system.

cond-mat.soft↗

arXiv2001

Rectification and Phase Locking for Particles on Two Dimensional Periodic Substrates

We show that a novel rectification phenomena is possible for overdamped particles interacting with a 2D periodic substrate and driven with a longitudinal DC drive and a circular AC drive. As a function of DC amplitude, the longitudinal velocity increases in a series of quantized steps with transverse rectification occuring near these transitions. We present a simple model that captures the quantization and rectification behaviors.

cond-mat.stat-mech↗

arXiv2001

Exact Multifractal Spectra for Arbitrary Laplacian Random Walks

Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, and of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge $c\leq 1$, with $c$ related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.

cond-mat.soft↗

arXiv2001

Growth Exponents with 3.99 Walkers

It is argued that the dielectric-breakdown model has an upper critical $η_c$ equal to 4, for which the clusters become one-dimensional. A renormalization group treatment of the model is presented near the critical $η$.

cond-mat.soft↗

arXiv2001

Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model

A fast method is presented for simulating the dielectric-breakdown model using iterated conformal mappings. Numerical results for the dimension and for corrections to scaling are in good agreement with the recent RG prediction of an upper critical $η_c=4$, at which a transition occurs between branching fractal clusters and one-dimensional nonfractal clusters.

cond-mat.soft↗

arXiv2001

Competition of Branches

We consider a general model of branch competition that automatically leads to a critical branching configuration. This model is inspired by the $4-η$ expansion of the dielectric breakdown model (DBM), but the mechanism of arriving at the critical point may be of relevance to other branching systems as well, such as fractures. The exact solution of this model clarifies the direct renormalization procedure used for the DBM, and demonstrates nonperturbatively the existence of additional irrelevant operators with complex scaling dimensions leading to discrete scale invariance. The anomalous exponents are shown to depend upon the details of branch interaction; we contrast with the branched growth model (BGM) in which these exponents are universal to lowest order in $1-ν$, and show that the BGM includes an inherent branch interaction different from that found in the DBM. We consider stationary and non-stationary regimes, corresponding to different growth geometries in the dielectric-breakdown model.

cond-mat↗

arXiv2000

Effective Gauge Theories of Spin Systems

A large variety of microscopic gauge theories can be written for antiferromagnetic spin systems, including $U(1), SU(2)$, and $Z_N$. I consider the question of the appropriate effective gauge theory for such systems. I show that while an SU(N) anti-ferromagnet can be written microscopically as a Z_N gauge theory, for unfrustrated systems, with a two-sublattice structure, there is always an effective U(1) gauge field. The dispersion relation for the gauge field is shown to depend on the presence or absence of charge-conjugation symmetry. Frustrated systems can break the gauge group to a discrete group, but this appears to always involve introducing a gap for the spinons.

cond-mat.str-el↗

arXiv2000

Breakdown of Conformal Invariance at Strongly Random Critical Points

We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a strongly random critical point. The average correlation functions of this system demonstrate a breakdown of conformal invariance, while the typical correlation functions demonstrate a breakdown of scale invariance. The breakdown of conformal invariance is due to the vanishing of the correlation functions at the infinite disorder fixed point, causing the critical correlation functions to be controlled by a dangerously irrelevant operator describing the approach to the fixed point. We relate the computation of average correlation functions to a problem of persistence in the RG flow.

cond-mat.dis-nn↗

arXiv2000

High-Dimensional Diffusive Growth

We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits a phase transition between ballistic and diffusion-controlled growth, with non-trivial corrections to cluster size at the critical point. Even in the ballistic regime, cluster scaling is controlled by extremal statistics due to the branching structure of the Cayley tree; it is the extremal nature of the fluctuations that enables us to solve the model.

cond-mat.soft↗

arXiv2000

Fermionic Mapping For Eigenvalue Correlation Functions Of (Weakly) Non-Hermitian Symplectic Ensemble

The eigenvalues of an arbitrary quaternionic matrix have a joint probability distribution function first derived by Ginibre. We show that there exists a mapping of this system onto a fermionic field theory and then use this mapping to integrate over the positions of the eigenvalues and obtain eigenvalue density as well as all higher correlation functions for both the strongly and weakly non-Hermitian cases.

cond-mat.dis-nn↗

arXiv2000

Dirac, Anderson, and Goldstone on the Kagome

We show that there exists a long-range RVB state for the kagome lattice spin-1/2 Heisenberg antiferromagnet for which the spinons have a massless Dirac spectrum. By considering various perturbations of the RVB state which give mass to the fermions by breaking a symmetry, we are able to describe a wide-ranging class of known states on the kagome lattice, including spin-Peierls solid and chiral spin liquid states. Using an RG treatment of fluctuations about the RVB state, we propose yet a different symmetry breaking pattern and show how collective excitations about this state account for the gapless singlet modes seen experimentally and numerically. We make further comparison with numerics for Chern numbers, dimer-dimer correlation functions, the triplet gap, and other quantities. To accomplish these calculations, we propose a variant of the SU(N) theory which enables us to include many of the effects of Gutzwiller projection at the mean-field level.

cond-mat.str-el↗

arXiv1999

The Dielectric Breakdown Model at Small $η$: Pole Dynamics

We consider the dielectric breakdown model in the limit $η\to 0^+$. A differential equation describing the surface growth is derived; this equation is KPZ plus a term causing linear instability, and includes a short-distance regularization similar to a viscosity. The equation exhibits an interesting dynamics in terms of poles, permitting us to derive a large family of solutions to the equation of motion. In terms of poles, we find all stationary configurations of the surface, and analytically calculate their stability. For each value of the viscosity, only one stable configuration is found, but this configuration is nonlinearly unstable in the presence of an exponentially small amount of noise. The present approach may be useful in understanding the dynamics for finite $η$, in particular the DLA model, in terms of perturbations to the infinitesimal $η$ problem.

cond-mat.soft↗

arXiv1999

Eigenvalue Distribution In The Self-Dual Non-Hermitian Ensemble

We consider an ensemble of self-dual matrices with arbitrary complex entries. This ensemble is closely related to a previously defined ensemble of anti-symmetric matrices with arbitrary complex entries. We study the two-level correlation functions numerically. Although no evidence of non-monotonicity is found in the real space correlation function, a definite shoulder is found. On the analytical side, we discuss the relationship between this ensemble and the $β=4$ two-dimensional one-component plasma, and also argue that this ensemble, combined with other ensembles, exhausts the possible universality classes in non-hermitian random matrix theory. This argument is based on combining the method of hermitization of Feinberg and Zee with Zirnbauer's classification of ensembles in terms of symmetric spaces.

cond-mat.dis-nn↗

arXiv1999

Renormalization Group for Large N Strongly Commensurate Dirty Boson Model

The large N sigma model, in D<4 space-time dimensions, with disorder a function of d space dimensions, is analyzed via a renormalization group treatment. Critical exponents for average quantities are calculated, first to lowest order and then to all orders, in $ε=D-2 - d/2$. In particular, it is found that $νd =2$. When D=d+1, this model is equivalent to a large N limit of the strongly commensurate dirty boson problem.

cond-mat.stat-mech↗

arXiv1999

Ground State and Spin Glass Phase of the Large N Infinite Range Spin Glass Via Supersymmetry

The large N infinite range spin glass is considered, in particular the number of spin components k needed to form the ground state and the sample-to-sample fluctuations in the Lagrange multiplier field on each site. The physical significance of k for the correlation functions is discussed. The difference between the large N and spherical spin glass is emphasized; a slight difference between the average Lagrange multiplier of the large N and spherical spin glasses is derived, leading to a slight increase in the energy of the ground state compared to the naive expectation. Further, there is a change in the low energy density of excitations in the large N system. A form of level repulsion, similar to that found in random matrix theory, is found to exist in this system, surviving interactions. Even though the system is an interacting one, a supersymmetric formalism is developed to deal with the problem of averaging over disorder.

cond-mat.dis-nn↗

arXiv1998

Bose Glass in Large N Commensurate Dirty Boson Model

The large N commensurate dirty boson model, in both the weakly and strongly commensurate cases, is considered via a perturbative renormalization group treatment. In the weakly commensurate case, there exists a fixed line under RG flow, with varying amounts of disorder along the line. Including 1/N corrections causes the system to flow to strong disorder, indicating that the model does not have a phase transition perturbatively connected to the Mott Insulator-Superfluid (MI-SF) transition. I discuss the qualitative effects of instantons on the low energy density of excitations. In the strongly commensurate case, a fixed point found previously is considered and results are obtained for higher moments of the correlation functions. To lowest order, correlation functions have a log-normal distribution. Finally, I prove two interesting theorems for large N vector models with disorder, relevant to the problem of replica symmetry breaking and frustration in such systems.

cond-mat.stat-mech↗

arXiv1997

Non-Hermitian Fermion Mapping for One-Component Plasma

The two-dimensional one-component logarithmic Coulomb gas is mapped onto a non-hermitian fermionic field theory. At $β=2$, the field theory is free. Correlation functions are calculated and a perturbation theory is discussed for extending to other $β$. A phase transition is found at the mean-field level at large $β$. Some results are extended to spaces of constant negative curvature.

cond-mat.stat-mech↗