Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect (2009)
Hastings, M. B., Loring, T. A.
For models of non-interacting fermions moving within sites arranged on a surface in three dimensional space, there can be obstructions to finding localized Wannier functions. We show that such...
Matrix Product States for dynamical simulation of infinite chains (2009)
Bañuls, M. C., Hastings, M. B., Verstraete, F., Cirac, J. I.
We propose a new method for computing the ground state properties and the time evolution of infinite chains based on a transverse contraction of the tensor network. The method does not require finite...
Light Cone Matrix Product (2009)
We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at $\Delta=0.5$, we simulate to...
Quantum Adiabatic Computation With a Constant Gap is Not Useful in One Dimension (2009)
We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic...
Entanglement vs. gap for one-dimensional spin systems (2009)
Gottesman, Daniel, Hastings, M. B.
We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement...
Matrix Product States for Dynamical Simulation of Infinite Chains (2009)
Bañuls, Mari Carmen, Hastings, M. B., Verstraete, F., Cirac, J. Ignacio
A Counterexample to Additivity of Minimum Output Entropy (2008)
We present a random construction of a pair of channels which gives, with non-zero probability for sufficiently large dimensions, a counterexample to the minimum output entropy conjecture. As shown by...
Making Almost Commuting Matrices Commute (2008)
Suppose two Hermitian matrices $A,B$ almost commute ($\Vert [A,B] \Vert \leq \delta$). Are they close to a commuting pair of Hermitian matrices, $A',B'$, with $\Vert A-A' \Vert,\Vert B-B'\Vert \leq...
Inference from Matrix Products: A Heuristic Spin Glass Algorithm (2008)
We present an algorithm for finding ground states of two dimensional spin glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero...
Synchronization and Dephasing of Many-Body States in Optical Lattices (2008)
Hastings, M. B., Levitov, L. S.
We introduce an approach to describe quantum-coherent evolution of a system of cold atoms in an optical lattice triggered by a change in superlattice potential. Using a time-dependent mean field...
Classical and Quantum Tensor Product Expanders (2008)
Hastings, M. B., Harrow, A. W.
We introduce the concept of quantum tensor product expanders. These are expanders that act on several copies of a given system, where the Kraus operators are tensor products of the Kraus operator on...
Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States (2008)
We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to...
Topology and Phases in Fermionic Systems (2007)
There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely...
Statistics of Partial Minima (2007)
Ben-Naim, E., Hastings, M. B., Izraelevitz, D.
Motivated by multi-objective optimization, we study extrema of a set of N points independently distributed inside the d-dimensional hypercube. A point in this set is k-dominated by another point when...
Quantum Belief Propagation (2007)
We present an accurate numerical algorithm, called quantum belief propagation (QBP), for simulation of one-dimensional quantum systems at non-zero temperature. The algorithm exploits the fact that...
Random Unitaries Give Quantum Expanders (2007)
We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically...
An Area Law for One Dimensional Quantum Systems (2007)
We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms...
Area laws in quantum systems: mutual information and correlations (2007)
Wolf, M. M., Verstraete, F., Hastings, M. B., Cirac, J. I.
The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. This counterintuitive idea which has its...
Entropy and Entanglement in Quantum Ground States (2007)
We consider the relationship between correlations and entanglement in gapped quantum systems, with application to matrix product state representations. We prove that there exist gapped...
We apply the technique of quasi-adiabatic continuation to study systems with continuous symmetries. We first derive a general form of Goldstone's theorem applicable to gapped nonrelativistic systems...
Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order (2006)
Bravyi, S., Hastings, M. B., Verstraete, F.
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails....
Community Detection as an Inference Problem (2006)
We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that...
Lieb-Robinson bounds and the generation of correlations and topological quantum order (2006)
Bravyi, S., Hastings, M. B., Verstraete, F.
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light-cone with exponentially decaying tails....
Conformal Invariance and SLE in Two-Dimensional Ising Spin Glasses (2006)
Amoruso, C., Hartmann, A. K., Hastings, M. B., Moore, M. A.
We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain...
Scaling in small-world resistor networks (2006)
Korniss, G., Hastings, M. B., Bassler, K. E., Berryman, M. J., Kozma, B., Abbott, Derek
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards–Wilkinson process on small-world networks, we obtain the...
Scaling in small-world resistor networks (2006)
Korniss, G., Hastings, M. B., Bassler, K. E., Berryman, M. J., Kozma, B., Abbott, Derek
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards–Wilkinson process on small-world networks, we obtain the...
Systematic Series Expansions for Processes on Networks (2005)
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network...
Solving Gapped Hamiltonians Locally (2005)
We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each...
Scaling in Small-World Resistor Networks (2005)
Korniss, G., Hastings, M. B., Bassler, K. E., Berryman, M. J., Kozma, B., Abbott, D.
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the...
Universal Scaling Relations in Strongly Anisotropic Materials (2005)
We consider the critical temperature in strongly anisotropic antiferromagnetic materials, with weak coupling between stacked planes, in order to determine the interplane coupling constant from...
Hastings, M. B., Wen, Xiao-Gang
We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density...
TOMOEDA,S., HASTINGS,M.B., MILLER,W.G.
The penetration of gamma rays into compartments of an aircraft carrier from two different radioisotopes was measured in 2 experiments. In 1 experiment, cobalt-60 and cesium-137 point isotropic...
Tomoeda,S., Frank,A. L., Hastings,M. B.
In order to correlate some basic measurements of radiation attenuation made on an aircraft carrier to other situations and geometries, experiments were carried out to study the effects of source...
Sufficient Conditions for Topological Order in Insulators (2004)
We prove the existence of low energy excitations in insulating systems at general filling factor under certain conditions, and discuss in which cases these may be identified as topological...
Intermittent polaron dynamics: Born-Oppenheimer out of equilibrium (2004)
Mozyrsky, D., Hastings, M. B., Martin, I.
We consider the non-equilibrium dynamics of a molecular level interacting with local phonon modes in the case of a strong polaronic shift which prevents a perturbative treatment of the problem....
Statistical Mechanics of Interfering Links (2004)
We consider the statistical mechanics of interfering transmissions in a wireless communications protocol. In this case, a connection between two nodes requires all other nodes within communication...
An $\epsilon$-expansion for Small-World Networks (2004)
I construct a well-defined expansion in $\epsilon=2-d$ for diffusion processes on small-world networks. The technique permits one to calculate the average over disorder of moments of the Green's...
Decay of Correlations in Fermi Systems at Non-zero Temperature (2004)
The locality of correlation functions is considered for Fermi systems at non-zero temperature. We show that for all short-range, lattice Hamiltonians, the correlation function of any two fermionic...
Locality in Quantum and Markov Dynamics on Lattices and Networks (2004)
We consider gapped systems governed by either quantum or Markov dynamics, with the low-lying states below the gap being approximately degenerate. For a broad class of dynamics, we prove that ground...
Spin-Orbit Scattering and Time-Reversal Symmetry: Detection of a Spin by Tunneling (2004)
We consider the possibility of detecting spin precession in a magnetic field by nonequilibrium transport processes. We find that time reversal symmetry imposes strong constraints on the problem....
Reichhardt, C., Reichhardt, C. J. Olson, Hastings, M. B.
We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an...
Renormalization of resonant tunneling in MOSFETs (2003)
Mozyrsky, D., Martin, I., Shnirman, A., Hastings, M. B.
We study tunneling between a localized defect state and a conduction band in the presence of strong electron-electron and electron-phonons interactions. We derive the tunneling rate as a function of...
Multiscaling at Point J: Jamming is a Critical Phenomenon (2003)
Drocco, J. A., Hastings, M. B., Reichhardt, C. J. Olson, Reichhardt, C.
We analyze the jamming transition that occurs as a function of increasing packing density in a disordered two-dimensional assembly of disks at zero temperature for ``Point J'' of the recently...
Testing the Collective Properties of Small-World Networks through Roughness Scaling (2003)
Kozma, B., Hastings, M. B., Korniss, G.
Motivated by a fundamental synchronization problem in scalable parallel computing and by a recent criterion for ``mean-field'' synchronizability in interacting systems, we study the Edwards-Wilkinson...
Glassy Ratchets for Collectively Interacting Particles (2003)
Reichhardt, C., Reichhardt, C. J. Olson, Hastings, M. B.
We show that ratchet effects can occur in a glassy media of interacting particles where there is no quenched substrate. We consider simulations of a disordered binary assembly of colloids in which...
Reichhardt, C. J. Olson, Hastings, M. B.
We propose an experiment for directly constructing and locally probing topologically entangled states of superconducting vortices which can be performed with present-day technology. Calculations...
Quantum limited sensitivity of SET-based displacement detectors (2003)
Mozyrsky, D., Martin, I., Hastings, M. B.
We consider a model of a quantum-mechanical resonator capacitively coupled to a single electron transistor (SET). The tunnel current in the SET is modulated by the vibrations of the resonator, and...
Lieb-Schultz-Mattis in Higher Dimensions (2003)
A generalization of the Lieb-Schultz-Mattis theorem to higher dimensional spin systems is shown. The physical motivation for the result is that such spin systems typically either have long-range...
Mean-Field and Anomalous Behavior on a Small-World Network (2003)
We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a...
Random Vibrational Networks and Renormalization Group (2002)
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case...
Ratchet Cellular Automata (2002)
Hastings, M. B., Reichhardt, C. J. Olson, Reichhardt, C.
In this work we propose a ratchet effect which provides a general means of performing clocked logic operations on discrete particles, such as single electrons or vortices. The states are propagated...
Depinning by Fracture in a Glassy Background (2002)
Hastings, M. B., Reichhardt, C. J. Olson, Reichhardt, C.
We force a single particle through a two-dimensional simulated glass. We find that the particle velocity obeys a robust power law that persists to drives well above threshold. As the single driven...
Quantum Dynamics in Non-equilibrium Strongly Correlated Environments (2002)
Hastings, M. B., Martin, I., Mozyrsky, D.
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...
Entropic Tightening of Vibrated Chains (2001)
Hastings, M. B., Daya, Z. A., Ben-Naim, E., Ecke, R. E.
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...
Exact Multifractal Spectra for Arbitrary Laplacian Random Walks (2001)
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...
Competition of Branches (2001)
We consider a general model of branch competition that automatically leads to a critical branching configuration. This model is inspired by the $4-\eta$ expansion of the dielectric breakdown model...
Growth Exponents with 3.99 Walkers (2001)
It is argued that the dielectric-breakdown model has an upper critical $\eta_c$ equal to 4, for which the clusters become one-dimensional. A renormalization group treatment of the model is presented...
Fractal to Nonfractal Phase Transition in the Dielectric Breakdown Model (2001)
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...
Breakdown of Conformal Invariance at Strongly Random Critical Points (2000)
Hastings, M. B., Sondhi, S. L.
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...
Effective Gauge Theories of Spin Systems (2000)
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...
High-Dimensional Diffusive Growth (2000)
Hastings, M. B., Halsey, Thomas C.
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...
Dirac, Anderson, and Goldstone on the Kagome (2000)
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...
The Dielectric Breakdown Model at Small $\eta$: Pole Dynamics (1999)
We consider the dielectric breakdown model in the limit $\eta\to 0^+$. A differential equation describing the surface growth is derived; this equation is KPZ plus a term causing linear instability,...
Eigenvalue Distribution In The Self-Dual Non-Hermitian Ensemble (1999)
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...
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...
Ground State and Spin Glass Phase of the Large N Infinite Range Spin Glass Via Supersymmetry (1999)
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...
Bose Glass in Large N Commensurate Dirty Boson Model (1998)
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,...
EXPERIMENTAL DATA OF GAMMA-RAY PENETRATION INTO THE COMPARTMENTS OF A LIGHT AIRCRAFT CARRIER. (1998)
Tomoeda,S., Hastings,M. B., Miller,W. G.
The penetration of gamma rays into compartments of an aircraft carrier from three different radioisotopes was measured. Co60, Cs137 and Ir192 sources were exposed on the Flight Deck and dosimeters...
Renormalization Group for Large N Strongly Commensurate Dirty Boson Model (1998)
The large N sigma model, in D
Non-Hermitian Fermion Mapping for One-Component Plasma (1997)
The two-dimensional one-component logarithmic Coulomb gas is mapped onto a non-hermitian fermionic field theory. At $\beta=2$, the field theory is free. Correlation functions are calculated and a...
Fermion Mapping for Orthogonal and Symplectic Ensembles (1996)
The circular orthogonal and circular symplectic ensembles are mapped onto free, non-hermitian fermion systems. As an illustration, the two-level form factors are calculated.
Bragg resonances for tunneling between edges of a 2D Quantum Hall system (1996)
Hastings, M. B., Levitov, L. S.
A theory is presented for tunneling between compressible regions on the sides of a narrow incompressible Quantum Hall strip. Assuming that electron interactions lead to formation of a Wigner crystal...
Laplacian growth as one-dimensional turbulence (1996)
Hastings, M. B., Levitov, L. S.
A new model of Laplacian stochastic growth is formulated using conformal mappings. The model describes two growth regimes, stable and turbulent, separated by a sharp phase transition. The first few...