arXiv subjects

K. S. D. Beach

Publications and source records attributed to K. S. D. Beach.

At least 19 recordsLinked to original sources

arXiv2024

Universal Aspects of Barrier Crossing Under Bias

The thermal activation process by which a system passes from one local energy minimum to another is a recurring motif in physics, chemistry, and biology. For instance, biopolymer chains are typically modeled in terms of energy landscapes, with folded and unfolded conformations represented by two distinct wells separated by a barrier. The rate of transfer between wells depends primarily on the height of the barrier, but it also depends on the details of the shape of the landscape along the trajectory. We consider the case of bias due to an external force, analogous to the pulling force applied in optical tweezer experiments on biopolymers. Away from the Arrhenius-law limit and well out of equilibrium, somewhat idiosyncratic behavior might be expected. Instead, we identify universal behavior of the biased activated-barrier-crossing process and demonstrate that data collapse onto a universal curve can be achieved for simulated data over a wide variety of energy landscapes having barriers of different height and shape and for loading rates spanning many orders of magnitude.

cond-mat.stat-mech↗

arXiv2024

Strongly Interacting Phases in Twisted Bilayer Graphene at the Magic Angle

Twisted bilayer graphene near the magic angle is known to have a cascade of insulating phases at integer filling factors of the low-energy bands. In this Letter we address the nature of these phases through an unrestricted, large-scale Hartree-Fock calculation on the lattice that self-consistently accounts for all electronic bands. Using numerically unbiased methods, we show that Coulomb interactions produce ferromagnetic insulating states at integer fillings $ν\in[-3,3]$ with maximal spin polarization $M_{\text{FM}}=4-|ν|$. We find that the $ν=0$ state is a pure ferromagnet, whereas all other insulating states are spin-valley polarized. At odd filling factors $|ν|=1,3$ those states have a quantum anomalous Hall effect with Chern number $\mathcal{C}=1$. Except for the $ν=0,-2$ states, all other integer fillings have insulating phases with additional sublattice symmetry breaking and antiferromagnetism in the remote bands. We map the metal-insulator transitions of these phases as a function of the effective dielectric constant. Our results establish the importance of large-scale lattice calculations to faithfully determine the ground states of TBG at integer fillings.

cond-mat.str-el↗

arXiv2021

Slow dynamics of the Fredkin spin chain

The dynamical behavior of a quantum many-particle system is characterized by the lifetime of its excitations. When the system is perturbed, observables of any non-conserved quantity decay exponentially, but those of a conserved quantity relax to equilibrium with a power law. Such processes are associated with a dynamical exponent $z$ that relates the spread of correlations in space and time. We present numerical results for the Fredkin model, a quantum spin chain with a three-body interaction term, which exhibits an unusually large dynamical exponent. We discuss our efforts to produce a reliable estimate $z$=3.16(1) through direct simulation of the quantum evolution and to explain the slow dynamics in terms of an excited bond that executes a constrained random walk in Monte Carlo time.

cond-mat.str-el↗

arXiv2020

Tunable quantum spin chain with three-body interactions

We introduce a generalization of the Fredkin spin chain with tunable three-body interactions expressed in terms of conventional spin-half operators. Of the model's two free parameters, one controls the preference for Ising antiferromagnetism and the other controls the strength of quantum fluctuations. In this formulation, the so-called $t$-deformed model (an exactly solvable, frustration-free Hamiltonian) lives on a unit circle centered on the origin of the phase diagram. The circle demarcates the boundary between ferromagnetic order inside and various antiferromagnetic phases outside. Throughout most of the non-ferromagnetic parts of the phase diagram, the ground state has Dyck word form: i.e., all contributing spin configurations exhibit perfect matching and nesting of spin up and spin down. The exceptions are two regions in which Dyck word mismatches are energetically favorable. We remark that in those regions the energy level spacing can be exponentially small in the system size. It is also the case that exact diagonalization reveals a highly idiosyncratic energy spectrum, presumably because the hard spin twist at the chain ends induces strong incommensurability effects on the bulk system when the chain length is small. As a convergence check, we benchmark our DMRG results to near-double-precision floating-point accuracy against analytical results at exactly solvable points and against exact diagonalization results for small system sizes across the entire parameter space.

cond-mat.str-el↗

arXiv2020

Reliable extraction of energy landscape properties from critical force distributions

The structural dynamics of a biopolymer is governed by a process of diffusion through its conformational energy landscape. In pulling experiments using optical tweezers, features of the energy landscape can be extracted from the probability distribution of the critical force at which the polymer unfolds. The analysis is often based on rate equations having Bell-Evans form, although it is understood that this modeling is inadequate and leads to unreliable landscape parameters in many common situations. Dudko and co-workers [Phys. Rev. Lett. 96, 108101 (2006)] have emphasized this critique and proposed an alternative form that includes an additional shape parameter (and that reduces to Bell-Evans as a special case). Their fitting function, however, is pathological in the tail end of the pulling force distribution, which presents problems of its own. We propose a modified closed-form expression for the distribution of critical forces that correctly incorporates the next-order correction in pulling force and is everywhere well behaved. Our claim is that this new expression provides superior parameter extraction and is valid even up to intermediate pulling rates. We present results based on simulated data that confirm its utility.

physics.bio-ph↗

arXiv2019

Effective interactions between local hopping modulations on the square lattice

We address the problem of free fermions interacting with frozen gauge fields. In particular, we consider a tight-binding model of fermions on the square lattice in which (i) flux 0 or $π$ is threaded through each plaquette and (ii) each nearest-neighbor link is decorated with an Ising degree of freedom that describes the local modulation of the hopping amplitude. Following the standard Ruderman--Kittel--Kasuya--Yosida (RKKY) approach, we compute an effective spin model in the coupling strength order by order. Unlike the original RRKY result for site-centered SU(2) spins in which the leading contribution is an effective exchange term at the second-order, perturbation theory in link-centered Z$_2$ case produces a first-order term that favors a collective ferromagnetic moment. If, by some means, an antiferromagnetic configuration can be stabilized, the energetics of ground state is controlled by an effective Ising interaction acting pairwise at the long range across the system.

cond-mat.str-el↗

arXiv2019

Deforming the Fredkin spin chain away from its frustration-free point

The Fredkin model describes a spin-half chain segment subject to three-body, correlated-exchange interactions and twisted boundary conditions. The model is frustration-free, and its ground state wave function is known exactly. Its low-energy physics is that of a strong xy ferromagnet with gapless excitations and an unusually large dynamical exponent. We study a generalized spin chain model that includes the Fredkin model as a special tuning point and otherwise interpolates between the conventional ferromagnetic and antiferromagnetic quantum Heisenberg models. We solve for the low-lying states, using exact diagonalization and density-matrix renormalization group calculations, in order to track the properties of the system as it is tuned away from the Fredkin point; we also present exact analytical results that hold right at the Fredkin point. We identify a zero-temperature phase diagram with multiple transitions and unexpected ordered phases. The Fredkin ground state turns out to be particularly brittle, unstable to even infinitesimal antiferromagnetic frustration. We remark on the existence of an "anti-Fredkin" point at which all the contributing spin configurations have a spin structure exactly opposite to those in the Fredkin ground state.

cond-mat.str-el↗

arXiv2017

Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions

Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo (QMC) simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transverse field Ising model. The ground state phase diagram, in which the tuning parameters are the transverse field and the coupling between fermion and Ising spins, is determined. At weak and intermediate coupling, a second-order Ising quantum phase transition and a first-order topological phase transition between two topologically distinct Dirac semimetals are observed. Interestingly, at the latter, the Dirac points smear out to form nodal lines in the Brillouin zone, and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced. At strong coupling, these two phase boundaries merge into a first-order transition.

cond-mat.str-el↗

arXiv2016

Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator

The strange correlator [Phys. Rev. Lett. 112, 247202 (2014)] has been proposed as a measure of symmetry protected topological order in one- and two-dimensional systems. It takes the form of a spin-spin correlation function, computed as a mixed overlap between the state of interest and a trivial local product state. We demonstrate that it can be computed exactly (asymptotically, in the Monte Carlo sense) for various Affleck-Kennedy-Lieb-Tasaki states by direct evaluation of the wave function within the valence bond loop gas framework. We present results for lattices with chain, square, honeycomb, cube, diamond, and hyperhoneycomb geometries. In each case, the spin quantum number S is varied such that 2S (the number of valence bonds emerging from each site) achieves various integer multiples of the lattice coordination number. We introduce the concept of strange correlator loop winding number and point to its utility in testing for the presence of symmetry protected topological order.

cond-mat.str-el↗

arXiv2015

Time-Resolved Mass Sensing of a Molecular Adsorbate Nonuniformly Distributed Along a Nanomechnical String

We show that the particular distribution of mass deposited on the surface of a nanomechanical resonator can be estimated by tracking the evolution of the device's resonance frequencies during the process of desorption. The technique, which relies on analytical models we have developed for the multimodal response of the system, enables mass sensing at much higher levels of accuracy than is typically achieved with a single frequency-shift measurement and no rigorous knowledge of the mass profile. We report on a series of demonstration experiments, in which the explosive molecule 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) is vapor deposited along the length of a silicon nitride nanostring to create a dense, random covering of RDX crystallites on the surface. In some cases, the deposition is biased to produce distributions with a slight excess or deficit of mass at the string midpoint. The added mass is then allowed to sublimate away under vacuum conditions, with the device returning to its original state over about 4 h (and the resonance frequencies, measured via optical interferometry, relaxing back to their pre-mass-deposition values). Our claim is that the detailed time trace of observed frequency shifts is rich in information---not only about the quantity of RDX initially deposited but also about its spatial arrangement along the nanostring. The data also reveal that sublimation in this case follows a nontrivial rate law, consistent with mass loss occurring at the exposed surface area of the RDX crystallites.

cond-mat.mes-hall↗

arXiv2013

Two distinct spin liquid states in a layered cubic lattice

We construct a family of short-range resonating-valence-bond wave functions on a layered cubic lattice, allowing for a tunable anisotropy in the amplitudes assigned to nearest-neighbour valence bonds along one axis. Monte Carlo simulations reveal that four phases are stabilized over the full range of the anisotropy parameter. They are separated from one another by a sequence of continuous quantum phase transitions. An antiferromagnetic phase, centred on the perfect isotropy point, intervenes between two distinct quantum spin liquid states. One of them is continuously deformable to the two-dimensional U(1) spin liquid, which is known to exhibit critical bond correlations. The other has both spin and bond correlations that decay exponentially. The existence of this second phase is proof that, contrary to expectations, neither a bipartite lattice structure nor a conventional Marshall sign rule is an impediment to realizing a fully gapped quantum spin liquid.

cond-mat.str-el↗

arXiv2013

Frustrating antiferromagnetic exchange interactions enhance specific valence-bond-pair motifs

We present variational results for the ground state of the antiferromagnetic quantum Heisenberg model with frustrating next-nearest-neighbour interactions. The trial wave functions employed are of resonating-valence-bond type, elaborated to account for various geometric motifs of adjacent bond pairs. The calculation is specialized to a square-lattice cluster consisting of just sixteen sites, large enough that the system can accommodate nontrivial singlet dimer correlations but small enough that exhaustive enumeration of states in the total spin zero sector is still feasible. A symbolic computation approach allows us to generate an algebraic expression for the expectation value of any observable and hence to carry out the energy optimization exactly. While we have no measurements that could unambiguously identify a spin liquid state in the controversial region at intermediate frustration, we can say that the bond-bond correlation factors that emerge do not appear to be consistent with the existence of a columnar valence bond crystal. Furthermore, our results suggest that the magnetically disordered region may accommodate two distinct phases.

cond-mat.str-el↗

arXiv2013

A general procedure for thermomechanical calibration of nano/micro-mechanical resonators

We provide a detailed description of a general procedure by which a nano/micro-mechanical resonator can be calibrated using its thermal motion. A brief introduction to the equations of motion for such a resonator is presented, followed by a detailed derivation of the corresponding power spectral density (PSD) function. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.

cond-mat.mes-hall↗

arXiv2013

Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure

We construct energy-optimized resonating valence bond wavefunctions as a means to sketch out the zero-temperature phase diagram of the square-lattice quantum Heisenberg model with competing nearest- (J1) and next-nearest-neighbour (J2) interactions. Our emphasis is not on achieving an accurate representation of the magnetically disordered intermediate phase (centred on a relative coupling g = J2/J1 ~ 1/2 and whose exact nature is still controversial) but on exploring whether and how the Marshall sign structure breaks down in the vicinity of the phase boundaries. Numerical evaluation of two- and four-spin correlation functions is carried out stochastically using a worm algorithm that has been modified to operate in either of two modes: one in which the sublattice labelling is fixed beforehand and another in which the worm manipulates the current labelling so as to sample various sign conventions. Our results suggest that the disordered phase evolves continuously out of the (pi,pi) Neel phase and largely inherits its Marshall sign structure; on the other hand, the transition from the magnetically ordered (pi,0) phase is strongly first order and involves an abrupt change in the sign structure and spatial symmetry as the results of a level crossing.

cond-mat.str-el↗

arXiv2012

High-Q Gold and Silicon Nitride Bilayer Nanostrings

Low-mass, high-Q, silicon nitride nanostrings are at the cutting edge of nanomechanical devices for sensing applications. Here we show that the addition of a chemically functionalizable gold overlayer does not adversely affect the Q of the fundamental out-of-plane mode. Instead the device retains its mechanical responsiveness while gaining sensitivity to molecular bonding. Furthermore, differences in thermal expansion within the bilayer give rise to internal stresses that can be electrically controlled. In particular, an alternating current excites resonant motion of the nanostring. This AC thermoelastic actuation is simple, robust, and provides an integrated approach to sensor actuation.

cond-mat.mes-hall↗

arXiv2012

Dissipation Mechanisms in Thermomechanically Driven Silicon Nitride Nanostrings

High-stress silicon nitride nanostrings are a promising system for sensing applications because of their ultra-high mechanical quality factors (Qs). By performing thermomechanical calibration across multiple vibrational modes, we are able to assess the roles of the various dissipation mechanisms in these devices. Specifically, we possess a set of nanostrings in which all measured modes fall upon a single curve of peak displacement versus frequency. This allows us to rule out bulk bending and intrinsic loss mechanisms as dominant sources of dissipation and to conclude that the most significant contribution to dissipation in high-stress nanostrings occurs at the anchor points.

cond-mat.mes-hall↗

arXiv2012

The BCS Pairing Instability in the Thermodynamic Limit

The superconducting pairing instability---as determined by a divergence of the two-particle susceptibility---is obtained in the mean field (BCS) approximation in the thermodynamic limit. The usual practice is to examine this property for a finite lattice. We illustrate that, while the conclusions remain unchanged, the technical features are very different in the thermodynamic limit and conform more closely with the usual treatment of phase transitions encountered in, for example, the mean-field paramagnetic-ferromagnetic transition. Furthermore, by going to the extreme dilute limit, one can distinguish three dimensions from one and two dimensions, in which a pairing instability occurs even for two particles.

cond-mat.supr-con↗

arXiv2010

Orbital-selective Mott transition and heavy fermion behavior in a bilayer Hubbard model for 3He

Inspired by recent experiments on 3He films between one and two atoms thick, we consider a bilayer Hubbard model on a triangular lattice. Our results are obtained in the framework of a cluster dynamical mean-field calculation with a quantum Monte Carlo impurity solver. For appropriate model parameters, we observe an enhancement of the effective mass as the first layer approaches integer filling and the second remains only partially filled. At finite temperatures, this increase of the effective mass -- or, equivalently, the decrease of the coherence temperature -- leads to a crossover to a state where the first layer fermions localize, drop out of the Luttinger volume, and generate essentially free local moments. This finite temperature behavior is shown to be robust against the cluster size above some critical temperature. The zero temperature phase diagram, however, depends on the cluster topology. In particular, for clusters with an even number of unit cells, the growth of the effective mass is cut off by a first-order, orbital-selective Mott transition.

cond-mat.str-el↗