Kevin S D Beach | University of Mississippi (original) (raw)

Papers by Kevin S D Beach

Physical Review B, 2016

The strange correlator [Phys. Rev. Lett. 112, 247202 (2014)] has been proposed as a measure of sy... more 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.

Abstract We present Exact Diagonalization calculations for the tJ model in small clusters with an... more Abstract We present Exact Diagonalization calculations for the tJ model in small clusters with an applied magnetic field perpendicular to the cluster. We show results of spin-spin correlations for 4× 4 clusters at different dopings and for different values of the parameter J ...

ABSTRACT Monte Carlo sampling of quantum spin models is only practical when it is possible to gau... more ABSTRACT Monte Carlo sampling of quantum spin models is only practical when it is possible to gauge away simultaneously all negative signs in the coefficients of the ground state wavefunction. The existence of such a transformation is related to the possibility of establishing a bipartite pattern of magnetic order on the lattice and to the choice of a so-called Marshall sign convention. In practice, identifying the correct Marshall sign convention is the responsibility of the QMC practitioner, and the convention itself is generally hard coded. It turns out, however, that a locally optimal sign convention can be determined dynamically within the simulation---meaning that for nonfrustrated systems the simulation quickly establishes a Marshall sign convention that leads to sign-problem-free sampling and that for frustrated systems the Marshall sign convention continually evolves in Monte Carlo time so as to minimize the severity of the sign problem. For concreteness, we focus on a worm algorithm formulated in the basis of singlet product states.

Biophysical Journal, 2014

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the times... more The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.

Physical Review Letters, 2014

The energy landscapes that drive structure formation in biopolymers are difficult to measure. Her... more The energy landscapes that drive structure formation in biopolymers are difficult to measure. Here we validate experimentally a novel method to reconstruct landscape profiles from single-molecule pulling curves using an inverse Weierstrass transform (IWT) of the Jarzysnki free-energy integral. The method was applied to unfolding measurements of a DNA hairpin, replicating the results found by the more-established weighted histogram (WHAM) and inverse Boltzmann methods. Applying both WHAM and IWT methods to reconstruct the folding landscape for a RNA pseudoknot having a stiff energy barrier, we found that landscape features with sharper curvature than the force probe stiffness could not be recovered with the IWT method. The IWT method is thus best for analyzing data from stiff force probes such as atomic force microscopes.

A Zeeman field affects the metallic heavy fermion ground state in two ways: (i) it splits the spi... more A Zeeman field affects the metallic heavy fermion ground state in two ways: (i) it splits the spin-degerenate conduction sea, leaving spin up and spin down Fermi surfaces with different band curvature; (ii) it competes with the Kondo effect and thus suppresses the mass enhancement. Taking these two effects into account, we compute the quasiparticle effective mass as a function of applied field strength within hybridization mean field theory. We also derive an expression for the optical conductivity, which is relevant to infrared spectroscopy measurements.

We present variational results for the ground state of the antiferromagnetic quantum Heisenberg m... more 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-valencebond 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.

A recent paper [Burovski et al., cond-mat/0507352] reports on a new, high-accuracy simulation of ... more A recent paper [Burovski et al., cond-mat/0507352] reports on a new, high-accuracy simulation of the classical φ 4 model (in the three-dimensional XY universality class). The authors claim that a careful scaling analysis of their data gives ν = 0.6711(1) for the thermal critical exponent. If correct, this would neatly resolve the discrepancy between numerical simulations and experiments on 4 He. There is reason, however, to doubt the accuracy of the result. A re-analysis of the data yields a significantly higher value of ν, one that is consistent with other Monte Carlo studies.

We study high-Q nanostrings that are joined end-to-end to form coupled linear arrays. Whereas iso... more We study high-Q nanostrings that are joined end-to-end to form coupled linear arrays. Whereas isolated individual resonators exhibit sinusoidal vibrational modes with an almost perfectly harmonic spectrum, the modes of the interacting strings are substantially hybridized. Even far-separated strings can show significantly correlated displacement. This remote coupling property is exploited to quantify the deposition of femtogram-scale masses with string-by-string positional discrimination based on measurements of one string only.

We provide a detailed description of a general procedure by which a nano/micro-mechanical resonat... more 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. arXiv:1305.0557v1 [cond-mat.mes-hall]

We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Sta... more We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves-in a manner dictated by the spin hamiltonian under consideration-toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J1-J2 antiferromagnetic Heisenberg model. Without frustration (J2 = 0), the amplitudes are radially symmetric and fall off as 1/r 3 in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J2/J1 0.418. It fails when the r = (2, 1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J2/J1 ≈ 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry.

Physical Review B, 2013

We construct energy-optimized resonating valence bond wave functions as a means to sketch out the... more We construct energy-optimized resonating valence bond wave functions as a means to sketch out the zerotemperature phase diagram of the square-lattice quantum Heisenberg model with competing nearest-(J 1 ) and next-nearest-neighbour (J 2 ) interactions. Our emphasis is not on achieving an accurate representation of the magnetically disordered intermediate phase (centred on a relative coupling g = J 2 /J 1 ∼ 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 (π, π) Néel phase and largely inherits its Marshall sign structure; on the other hand, the transition from the magnetically ordered (π, 0) phase is strongly first order and involves an abrupt change in the sign structure and spatial symmetry as the result of a level crossing.

The European Physical Journal B, 2000

We examine the role of spin twists in the formation of domain walls, often called stripes, by foc... more We examine the role of spin twists in the formation of domain walls, often called stripes, by focusing on the spin textures found in the cluster spin glass phases of La2−xSrxCuO4 and Y1−xCaxBa2Cu3O6. To this end, we derive an analytic expression for the spin distortions produced by a frustrating bond, both near the core region of the bond and in the far field, and then derive an expression for interaction energies between such bonds. We critique our analytical theory by comparison to numerical solutions of this problem and find excellent agreement. By looking at collections of small numbers of such bonds localized in some region of a lattice, we demonstrate the stability of small "clusters" of spins, each cluster having its own orientation of its antiferromagnetic order parameter. Then, we display a domain wall corresponding to spin twists between clusters of locally ordered spins showing how spin twists can serve as a mechanism for stripe formation. Since the charges are localized in this model, we emphasize that these domain walls are produced in a situation for which no kinetic energy is present in the problem.

Applied Physics Letters, 2012

Low-mass, high-Q, silicon nitride nanostrings are at the cutting edge of nanomechanical devices f... more 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 (AC) excites resonant motion of the nanostring. This AC thermoelastic actuation is simple, robust, and provides an integrated approach to sensor actuation. arXiv:1207.5790v2 [cond-mat.mes-hall]

Physical Review B, 2016

The strange correlator [Phys. Rev. Lett. 112, 247202 (2014)] has been proposed as a measure of sy... more 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.

Abstract We present Exact Diagonalization calculations for the tJ model in small clusters with an... more Abstract We present Exact Diagonalization calculations for the tJ model in small clusters with an applied magnetic field perpendicular to the cluster. We show results of spin-spin correlations for 4× 4 clusters at different dopings and for different values of the parameter J ...

ABSTRACT Monte Carlo sampling of quantum spin models is only practical when it is possible to gau... more ABSTRACT Monte Carlo sampling of quantum spin models is only practical when it is possible to gauge away simultaneously all negative signs in the coefficients of the ground state wavefunction. The existence of such a transformation is related to the possibility of establishing a bipartite pattern of magnetic order on the lattice and to the choice of a so-called Marshall sign convention. In practice, identifying the correct Marshall sign convention is the responsibility of the QMC practitioner, and the convention itself is generally hard coded. It turns out, however, that a locally optimal sign convention can be determined dynamically within the simulation---meaning that for nonfrustrated systems the simulation quickly establishes a Marshall sign convention that leads to sign-problem-free sampling and that for frustrated systems the Marshall sign convention continually evolves in Monte Carlo time so as to minimize the severity of the sign problem. For concreteness, we focus on a worm algorithm formulated in the basis of singlet product states.

Biophysical Journal, 2014

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the times... more The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.

Physical Review Letters, 2014

The energy landscapes that drive structure formation in biopolymers are difficult to measure. Her... more The energy landscapes that drive structure formation in biopolymers are difficult to measure. Here we validate experimentally a novel method to reconstruct landscape profiles from single-molecule pulling curves using an inverse Weierstrass transform (IWT) of the Jarzysnki free-energy integral. The method was applied to unfolding measurements of a DNA hairpin, replicating the results found by the more-established weighted histogram (WHAM) and inverse Boltzmann methods. Applying both WHAM and IWT methods to reconstruct the folding landscape for a RNA pseudoknot having a stiff energy barrier, we found that landscape features with sharper curvature than the force probe stiffness could not be recovered with the IWT method. The IWT method is thus best for analyzing data from stiff force probes such as atomic force microscopes.

A Zeeman field affects the metallic heavy fermion ground state in two ways: (i) it splits the spi... more A Zeeman field affects the metallic heavy fermion ground state in two ways: (i) it splits the spin-degerenate conduction sea, leaving spin up and spin down Fermi surfaces with different band curvature; (ii) it competes with the Kondo effect and thus suppresses the mass enhancement. Taking these two effects into account, we compute the quasiparticle effective mass as a function of applied field strength within hybridization mean field theory. We also derive an expression for the optical conductivity, which is relevant to infrared spectroscopy measurements.

We present variational results for the ground state of the antiferromagnetic quantum Heisenberg m... more 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-valencebond 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.

A recent paper [Burovski et al., cond-mat/0507352] reports on a new, high-accuracy simulation of ... more A recent paper [Burovski et al., cond-mat/0507352] reports on a new, high-accuracy simulation of the classical φ 4 model (in the three-dimensional XY universality class). The authors claim that a careful scaling analysis of their data gives ν = 0.6711(1) for the thermal critical exponent. If correct, this would neatly resolve the discrepancy between numerical simulations and experiments on 4 He. There is reason, however, to doubt the accuracy of the result. A re-analysis of the data yields a significantly higher value of ν, one that is consistent with other Monte Carlo studies.

We study high-Q nanostrings that are joined end-to-end to form coupled linear arrays. Whereas iso... more We study high-Q nanostrings that are joined end-to-end to form coupled linear arrays. Whereas isolated individual resonators exhibit sinusoidal vibrational modes with an almost perfectly harmonic spectrum, the modes of the interacting strings are substantially hybridized. Even far-separated strings can show significantly correlated displacement. This remote coupling property is exploited to quantify the deposition of femtogram-scale masses with string-by-string positional discrimination based on measurements of one string only.

We provide a detailed description of a general procedure by which a nano/micro-mechanical resonat... more 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. arXiv:1305.0557v1 [cond-mat.mes-hall]

We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Sta... more We describe a "master equation" analysis for the bond amplitudes h(r) of an RVB wavefunction. Starting from any initial guess, h(r) evolves-in a manner dictated by the spin hamiltonian under consideration-toward a steady-state distribution representing an approximation to the true ground state. Unknown transition coefficients in the master equation are treated as variational parameters. We illustrate the method by applying it to the J1-J2 antiferromagnetic Heisenberg model. Without frustration (J2 = 0), the amplitudes are radially symmetric and fall off as 1/r 3 in the bond length. As the frustration increases, there are precursor signs of columnar or plaquette VBS order: the bonds preferentially align along the axes of the square lattice and weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule holds over a large range of couplings, J2/J1 0.418. It fails when the r = (2, 1) bond amplitude first goes negative, a point also marked by a cusp in the ground state energy. A nonrigourous extrapolation of the staggered magnetic moment (through this point of nonanalyticity) shows it vanishing continuously at a critical value J2/J1 ≈ 0.447. This may be preempted by a first-order transition to a state of broken translational symmetry.

Physical Review B, 2013

We construct energy-optimized resonating valence bond wave functions as a means to sketch out the... more We construct energy-optimized resonating valence bond wave functions as a means to sketch out the zerotemperature phase diagram of the square-lattice quantum Heisenberg model with competing nearest-(J 1 ) and next-nearest-neighbour (J 2 ) interactions. Our emphasis is not on achieving an accurate representation of the magnetically disordered intermediate phase (centred on a relative coupling g = J 2 /J 1 ∼ 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 (π, π) Néel phase and largely inherits its Marshall sign structure; on the other hand, the transition from the magnetically ordered (π, 0) phase is strongly first order and involves an abrupt change in the sign structure and spatial symmetry as the result of a level crossing.

The European Physical Journal B, 2000

We examine the role of spin twists in the formation of domain walls, often called stripes, by foc... more We examine the role of spin twists in the formation of domain walls, often called stripes, by focusing on the spin textures found in the cluster spin glass phases of La2−xSrxCuO4 and Y1−xCaxBa2Cu3O6. To this end, we derive an analytic expression for the spin distortions produced by a frustrating bond, both near the core region of the bond and in the far field, and then derive an expression for interaction energies between such bonds. We critique our analytical theory by comparison to numerical solutions of this problem and find excellent agreement. By looking at collections of small numbers of such bonds localized in some region of a lattice, we demonstrate the stability of small "clusters" of spins, each cluster having its own orientation of its antiferromagnetic order parameter. Then, we display a domain wall corresponding to spin twists between clusters of locally ordered spins showing how spin twists can serve as a mechanism for stripe formation. Since the charges are localized in this model, we emphasize that these domain walls are produced in a situation for which no kinetic energy is present in the problem.

Applied Physics Letters, 2012

Low-mass, high-Q, silicon nitride nanostrings are at the cutting edge of nanomechanical devices f... more 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 (AC) excites resonant motion of the nanostring. This AC thermoelastic actuation is simple, robust, and provides an integrated approach to sensor actuation. arXiv:1207.5790v2 [cond-mat.mes-hall]