arXiv subjects

Christopher L. Henley

Publications and source records attributed to Christopher L. Henley.

36 records · Page 2Linked to original sources

arXiv2009

Exact ground states and correlation functions of chain and ladder models of interacting hardcore bosons or spinless fermions

By removing one empty site between two occupied sites, we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest-neighbor repulsion respectively, and ultimately in terms of the one-dimensional Fermi sea. We then introduce the intervening-particle expansion, where we write correlation functions in such ground states as a systematic sum over conditional expectations, each of which can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various ground-state correlation functions are calculated for the bosonic and fermionic chains with infinite nearest-neighbor repulsion, as well as for a ladder model of spinless fermions with infinite nearest-neighbor repulsion and correlated hopping in three limiting cases. We find that the decay of these correlation functions are governed by surprising power-law exponents.

cond-mat.str-el↗

arXiv2009

Anharmonic Ground state selection in the pyrochlore antiferromagnet

In the pyrochlore lattice Heisenberg antiferromagnet, for large spin length $S$, the massive classical ground state degeneracy is partly lifted by the zero-point energy of quantum fluctuations at harmonic order in spin-waves. However, there remains an infinite manifold of degenerate collinear ground states, related by a gaugelike symmetry. We have extended the spin-wave calculation to quartic order, assuming a Gaussian variational wavefunction (equivalent to Hartree-Fock approximation). Quartic calculations \emph{do} break the harmonic-order degeneracy of periodic ground states. The form of the effective Hamiltonian describing this splitting, which depends on loops, was fitted numerically and also rationalized analytically. We find a family of states that are still almost degenerate, being split by the term from loops of length 26. We also calculated the anharmonic terms for the checkerboard lattice, and discuss why it (as well as the kagomé lattice) behave differently than the pyrochlore at anharmonic orders.

cond-mat.str-el↗

arXiv2008

Possible mechanisms for initiating macroscopic left-right asymmetry in developing organisms

How might systematic left-right (L/R) asymmetry of the body plan originate in multicellular animals (and plants)? Somehow, the microscopic handedness of biological molecules must be brought up to macroscopic scales. Basic symmetry principles suggest that the usual "biological" mechanisms -- diffusion and gene regulation -- are insufficient to implement the "right-hand rule" defining a third body axis from the other two. Instead, on the cellular level, "physical" mechanisms (forces and collective dynamic states) are needed involving the long stiff fibers of the cytoskeleton. I discuss some possible scenarios; only in the case of vertebrate internal organs is the answer currently known (and even that is in dispute).

q-bio.TO↗

arXiv2008

Depleted pyrochlore antiferromagnets

I consider the class of "depleted pyrochlore" lattices of corner-sharing triangles, made by removing spins from a pyrochlore lattice such that every tetrahedron loses exactly one. Previously known examples are the "hyperkagome" and "kagome staircase". I give criteria in terms of loops for whether a given depleted lattice can order analogous to the kagome \sqrt{3} \times \sqrt{three} state, and also show how the pseudo-dipolar correlations (due to local constraints) generalize to even the random depleted case.

cond-mat.stat-mech↗

arXiv2006

Effective Hamiltonians for large-S pyrochlore antiferromagnet

The pyrochlore lattice Heisenberg antiferromagnet has a massive classical ground state degeneracy. We summarize three approximation schemes, valid for large spin length $S$, to capture the (partial) lifting of this degeneracy when zero-point quantum fluctuations are taken into account; all three are related to analytic loop expansions. The first is harmonic order spin waves; at this order, there remains an infinite manifold of degenerate collinear ground states, related by a gauge-like symmetry. The second is anharmonic (quartic order) spin waves, using a self-consistent approximation; the harmonic-order degeneracy is split, but (within numerical precision) some degeneracy may remain, with entropy still of order $L$ in a system of $L^3$ sites. The third is a large-N approximation, a standard and convenient approach for frustrated antiferromagnets; however, the large-N result contradicts the harmonic order at $O(S)$ hence must be wrong (for large $S$).

cond-mat.str-el↗

arXiv2006

Many-Body Density Matrices On a Two-Dimensional Square Lattice: Noninteracting and Strongly Interacting Spinless Fermions

The reduced density matrix of an interacting system can be used as the basis for a truncation scheme, or in an unbiased method to discover the strongest kind of correlation in the ground state. In this paper, we investigate the structure of the many-body fermion density matrix of a small cluster in a square lattice. The cluster density matrix is evaluated numerically over a set of finite systems, subject to non-square periodic boundary conditions given by the lattice vectors $\bR_1 \equiv (R_{1x}, R_{1y})$ and $\bR_2 \equiv (R_{2x}, R_{2y})$. We then approximate the infinite-system cluster density-matrix spectrum, by averaging the finite-system cluster density matrix (i) over degeneracies in the ground state, and orientations of the system relative to the cluster, to ensure it has the proper point-group symmetry; and (ii) over various twist boundary conditions to reduce finite size effects. We then compare the eigenvalue structure of the averaged cluster density matrix for noninteracting and strongly-interacting spinless fermions, as a function of the filling fraction $\nbar$, and discuss whether it can be approximated as being built up from a truncated set of single-particle operators.

cond-mat.str-el↗

arXiv2005

Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length $S$ is a highly frustrated model with an macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic order) spin wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating {\it effective Hamiltonian}, acting within the subspace of Ising spin configurations representing the {\it collinear} ground states. It consists of products of Ising spins around loops, i.e has the form of a $Z_2$ lattice gauge theory. The remaining ground state entropy is still infinite but not extensive, being $O(L)$ for system size $O(L^3)$. All these ground states have unit cells bigger than those considered previously.

cond-mat.str-el↗

arXiv2003

Many-Body Density Matrices for Free Fermions

Building upon an analytical technique introduced by Chung and Peschel [M. Chung and I. Peschel, Phys. Rev. B 64, art. 064412 (2001)], we calculated the density matrix rho_B of a finite block of B sites within an infinite system of free spinless fermions. In terms of the block Green function matrix G (whose elements are G_ij = < c_i^+ c_j>, where c_i^+ and c_j are fermion creation and annihilation operators acting on sites i and j within the block respectively), the density matrix can be written as rho_B = det(1 - G) exp[ sum_ij (log G(1 - G^{-1})_ij c_i^+ c_j]. Implications of such a result to Hilbert space truncation for real-space renormalization schemes is discussed.

cond-mat↗

arXiv2003

Operator-Based Truncation Scheme Based on the Many-Body Fermion Density Matrix

In [S. A. Cheong and C. L. Henley, cond-mat/0206196 (2002)], we found that the many-particle eigenvalues and eigenstates of the many-body density matrix $ρ_B$ of a block of $B$ sites cut out from an infinite chain of noninteracting spinless fermions can all be constructed out of the one-particle eigenvalues and one-particle eigenstates respectively. In this paper we developed a statistical-mechanical analogy between the density matrix eigenstates and the many-body states of a system of noninteracting fermions. Each density matrix eigenstate corresponds to a particular set of occupation of single-particle pseudo-energy levels, and the density matrix eigenstate with the largest weight, having the structure of a Fermi sea ground state, unambiguously defines a pseudo-Fermi level. We then outlined the main ideas behind an operator-based truncation of the density matrix eigenstates, where single-particle pseudo-energy levels far away from the pseudo-Fermi level are removed as degrees of freedom. We report numerical evidence for scaling behaviours in the single-particle pseudo-energy spectrum for different block sizes $B$ and different filling fractions $\nbar$. With the aid of these scaling relations, which tells us that the block size $B$ plays the role of an inverse temperature in the statistical-mechanical description of the density matrix eigenstates and eigenvalues, we looked into the performance of our operator-based truncation scheme in minimizing the discarded density matrix weight and the error in calculating the dispersion relation for elementary excitations. This performance was compared against that of the traditional density matrix-based truncation scheme, as well as against a operator-based plane wave truncation scheme, and found to be very satisfactory.

cond-mat.str-el↗

arXiv2003

From classical to quantum dynamics at Rokhsar-Kivelson points

For any classical statistical-mechanics model with a discrete state space, and endowed with a dynamics satisfying detailed balance, it is possible to generalize the Rokhsar-Kivelson point for the quantum dimer model. That is, a quantum Hamiltonian can be constructed (on the same state space), such that the ground state wavefunction coincides with the classical equilibrium distribution. Furthermore the excited eigenstates correspond to classical relaxation modes, which (in cases with a symmetry or conserved quantity) permits extraction of the dispersion law of long-wavelength excitations. The mapping is natural mainly when the states have equal weight, as is typical of a highly frustrated model. Quantum and classical correlation functions are related by analytic continuation to the imaginary time axis.

cond-mat.str-el↗

arXiv2002

Classical Mechanics of a Three Spin Cluster

A cluster of three spins coupled by single-axis anisotropic exchange exhibits classical behaviors ranging from regular motion at low and high energies, to chaotic motion at intermediate energies. A change of variable, taking advantage of the conserved z-angular momentum, combined with a 3-d graphical presentation (described in the Appendix), produce Poincare sections that manifest all symmetries of the system and clearly illustrate the transition to chaos as energy is increased. The three-spin system has four families of periodic orbits. Linearization around stationary points predicts orbit periods in the low energy (antiferromagnetic) and high energy (ferromagnetic) limits and also determines the stability properties of certain orbits at a special intermediate energy. The energy surface undergoes interesting changes of topology as energy is varied. We describe the similiarities of our three spin system with the Anisotropic Kepler Problem and the Henon-Heiles Hamiltonian. An appendix discusses numerical integration techniques for spin systems.

nlin.CD↗

arXiv2002

Total-energy-based structure prediction for d(AlNiCo)

One may predict a quasicrystal structure starting from electrons and quantum mechanics, as approximated by interatomic pair potentials calibrated with ab-initio total-energy calculations, combined with the experimentally known composition and lattice constants. Here we report our progress on the "basic Ni" decagonal phase d(Al70 Ni21 Co9). Atomic configurations are represented as decorations of (possibly) random tilings. Our method was Monte Carlo simulation using both lattice-gas hops by atoms and tile-flip rearrangements, eventually followed by molecular dynamics and relaxation of the atom positions. Initially allowing the greatest freedom of atom positions, we observed nearly deterministic structural rules and enforced these as constraints involving larger tiles; this procedure was repeated at the next level of modeling. In crude and preliminary form, the effective Hamiltonian for tile-tile interactions is known, which is needed for further simulations to infer the long-range order. Our atomic arrangements in the 20 A decagonal cluster are compared with three structure models based on recent experiments.

cond-mat↗

arXiv2000

Effective Hamiltonians and dilution effects in kagome and related antiferromagnets

What is the zero-temperature ordering pattern of a Heisenberg antiferromagnet with large spin length $S$ (and possibly small dilution), on the kagome lattice, or others built from corner-sharing triangles and tetrahedra? First, I summarize the uses of effective Hamiltonians to resolve the large ground-state degeneracy, leading to long-range order of the usual kind. Secondly, I discuss the effects of dilution, in particular to {\it non}-frustration of classical ground states, in that every simplex of spins is optimally satisfied. Of three explanations for this, the most complete is Moessner-Chalker constraint-counting. Quantum zero-point energy may compete with classical exchange energy in a diluted system, creating frustration and enabling a spin-glass state. I suggest that the regime of over 97% occupation is qualitatively different from the more strongly diluted regime.

cond-mat↗

arXiv1998

Semiclassical eigenstates of four-sublattice antiferromagnets

Applying Bohr-Sommerfeld quantization and the topological phase of spin path integrals, one can determine the multiplicities, lattice symmetries, and eigenvalue clustering pattern of the low-lying singlet eigenstates of the triangular and fcc antiferromagnets with 4-sublattice classical ground states. In the triangular case, the clustering pattern agrees with numerical results of Lecheminant et al (Phys. Rev. B 52, 6647 (1995)).

cond-mat↗

arXiv1998

Effective potentials for 6-coordinated Boron: a structural approach

We have built an ab-initio LDA energy database with over 60 hypothetical extended structures of pure Boron, in each of which the coordination environment of each atom is equivalent. Focusing on eleven 6-coordinated structures, which are most relevant to the observed Boron phases, we deduce a nearest-neighbor-only 2-body interaction, refined by potentials that depend on angles and asymmetry within the local atomic environment. The resulting effective potentials describe the 6-coordinated structures with an average error of 0.1 eV/atom, and favor the environment most often seen in real Boron.

cond-mat.mtrl-sci↗

arXiv1996

A new binary decagonal Frank-Kasper quasicrystal phase

A structure model of atoms of two sizes, interacting with Lennard-Jones potentials and simulated by molecular dynamics, was observed to freeze into a decagonal quasicrystal dominated by Frank-Kasper coordination shells and closely related to the Henley-Elser model for icosahedral quasicrystals. Idealized structure models can be described as decorations of triangle-rectangle and rhombus tilings. Equilibrium properties of the idealized model have been determined by molecular dynamics simulations and a high stability of the model and a low jump rate of the atoms have also been observed.

cond-mat↗

arXiv1992

Spin tunneling in the Kagomé antiferromagnet

The collective tunneling of a small cluster of spins between two degenerate ground state configurations of the Kagomé-lattice quantum Heisenberg antiferromagnet is \mbox{studied}. The cluster consists of the six spins on a hexagon of the lattice. The resulting tunnel splitting energy $Δ$ is calculated in detail, including the prefactor to the exponential $\exp(- \SSo / \hbar)$. This is done by setting up a coherent spin state path integral in imaginary time and evaluating it by the method of steepest descent. The hexagon tunneling problem is mapped onto a much simpler tunneling problem, involving only one collective degree of freedom, which can be treated by known methods. It is found that for half-odd-integer spins, the tunneling amplitude and the tunnel splitting energy are exactly zero, because of destructive interference between symmetry-related $(+)$-instanton and $(-)$-instanton tunneling paths. This destructive interference is shown to occur also for certain larger loops of spins on the Kagomé lattice. For small, integer spins, our results suggest that tunneling strongly competes with \mbox{in-plane} order-from-disorder selection effects; it constitutes a disordering mechanism that might drive the system into a partially disordered ground state, related to a spin nematic.

cond-mat↗

arXiv1992

Destructive quantum interference in spin tunneling problems

In some spin tunneling problems, there are several different but symmetry-related tunneling paths that connect the same initial and final configurations. The topological phase factors of the corresponding tunneling amplitudes can lead to destructive interference between the different paths, so that the total tunneling amplitude is zero. In the study of tunneling between different ground state configurations of the Kagomé-lattice quantum Heisenberg antiferromagnet, this occurs when the spin $s$ is half-odd-integer.

cond-mat↗