arXiv subjects

S. H. Curnoe

Publications and source records attributed to S. H. Curnoe.

At least 19 recordsLinked to original sources

arXiv2025

Mixed state concurrence for symmetric systems

We present a method to quantify entanglement in mixed states of highly symmetric systems. Symmetry constrains interactions between parts and predicts the degeneracies of the states. While symmetry alone produces entangled eigenstates, the thermal mixed state (density) which contains all of the eigenstate densities weighted by their Boltzmann factors is not necessarily as entangled as the eigenstates themselves because generally the mixed state can be re-expressed as a sum over densities which are less entangled. The entanglement of the mixed state is the minimum obtained by considering all such re-expressions, but there is no well-defined approach to solving this problem generally. Our method uses symmetry to explicitly construct unentangled densities, which are then optimally included in the thermal mixed state, resulting in a quantitative measure of entanglement that accounts for the reduction of entanglement arising from degenerate states. We present results for several small spin systems.

quant-ph↗

arXiv2024

Concurrence and entanglement on a 16-site spin-1/2 pyrochlore cluster

We examine the entanglement of the ground state of a 16-site spin-1/2 pyrochlore cluster in the quantum spin ice regime via various calculations of ${\cal I}$-concurrence. Exact ground state solutions to a quantum spin Hamiltonian with four nearest-neighbour exchange parameters were obtained using exact diagonalization. We present results for the ground state ${\cal I}$-concurrence in a region within the parameter space of the model where the ground state is a singlet. We discuss variations in the ${\cal I}$-concurrence in the context of the composition of the ground state and we demonstrate how a lattice distortion disentangles the state.

cond-mat.str-el↗

arXiv2023

Symmetry considerations in exact diagonalization: spin-1/2 pyrochlore magnets

We describe how the methods of group theory (symmetry) are used to optimize the problem of exact diagonalization of a quantum system on a 16-site pyrochlore lattice. By analytically constructing a complete set of symmetrized states, we completely block-diagonalize the Hamiltonian. As an example, we consider a spin-1/2 system with nearest neighbour exchange interactions.

cond-mat.str-el↗

arXiv2022

Exact diagonalization for spin-1/2 spin ice pyrochlores

We find exact solutions to the Hamiltonian of a 16-site spin-1/2 pyrochlore crystal with nearest neighbour exchange interactions. The methods of group theory (symmetry) are used to completely block-diagonalize the Hamiltonian, yielding precise details about symmetry of the eigenstates, in particular those components which are {\em spin ice} states, in order to evaluate the spin ice density at finite temperature. At low enough temperatures, a `perturbed' spin ice phase is clearly outlined within the four parameter space of the general model of exchange interactions. The quantum spin ice phase is expected to exist outside these boundaries.

cond-mat.str-el↗

arXiv2021

A general model of MnSi-like spiral magnets

A general, symmetry-allowed model of nearest-neighbour interactions for MnSi-like magnets is presented. A left-handed helical magnet phase occurs within a large parameter space of the model, which is explored via numerical simulation. The relations between microscopic features of the spiral structure and various model parameters, including an external magnetic field, are determined and show good agreement with predictions from free energy considerations. A skyrmion structure is stabilized near the boundary.

cond-mat.str-el↗

arXiv2020

Analytic description of spin waves in dipolar/octupolar pyrochlore magnets

We derive analytic forms for spin waves in pyrochlore magnets with dipolar-octupolar interactions, such as ${\rm Nd}_2{\rm Zr}_2{\rm O}_7$. We obtain full knowledge of the diagonalized magnonic Hamiltonian within the linear spin wave approximation. We also consider the effect of a "breathing mode" as a perturbation of this system. The breathing mode lifts the degeneracy of the upper band of the spin wave dispersion along the direction $X\to W$ in $k$-space.

cond-mat.str-el↗

arXiv2020

Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions

We systematically generate the perturbative expansion for the two-particle spin susceptibility in the Feynman diagrammatic formalism and apply this expansion to a model system - the single-band Hubbard model on a square lattice. We make use of algorithmic Matsubara integration (AMI) [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019)] to analytically evaluate Matsubara frequency summations, allowing us to symbolically impose analytic continuation to the real frequency axis. We minimize our computational expense by applying graph invariant transformations [Amir Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 101, 125109 (2020)]. We highlight extensions of the random-phase approximation and T-matrix methods that, due to AMI, become tractable. We present results for weak interaction strength where the direct perturbative expansion is convergent, and verify our results on the Matsubara axis by comparison to other numerical methods. By examining the spin susceptibility as a function of real-frequency via an order-by-order expansion we can identify precisely what role higher order corrections play on spin susceptibility and demonstrate the utility and limitations of our approach.

cond-mat.str-el↗

arXiv2019

Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure

We present a general method to optimize the evaluation of Feynman diagrammatic expansions, which requires the automated symbolic assignment of momentum/energy conserving variables to each diagram. With this symbolic representation, we utilize the pole structure of each diagram to automatically sort the Feynman diagrams into groups that are likely to contain nearly equal or nearly cancelling diagrams, and we show that for some systems this cancellation is exact. This allows for a potentially massive cancellation during the numerical integration of internal momenta variables, leading to an optimal suppression of the `sign problem' and hence reducing the computational cost. Although we define these groups using a frequency space representation, the equality or cancellation of diagrams within the group remains valid in other representations such as imaginary time used in standard diagrammatic Monte Carlo. As an application of the approach we apply this method, combined with algorithmic Matsubara integration (AMI) [Phys. Rev. B 99, 035120 (2019)] and Monte Carlo methods, to the Hubbard model self-energy expansion on a 2D square lattice up to sixth order which we evaluate and compare with existing benchmarks.

cond-mat.str-el↗

arXiv2018

Algorithmic Matsubara Integration for Hubbard-like models

We present an algorithm to evaluate Matsubara sums for Feynman diagrams comprised of bare Green's functions with single-band dispersions with local U Hubbard interaction vertices. The algorithm provides an exact construction of the analytic result for the frequency integrals of a diagram that can then be evaluated for all parameters $U$, temperature $T$, chemical potential $μ$, external frequencies and internal/external momenta. This method allows for symbolic analytic continuation of results to the real frequency axis, avoiding any ill-posed numerical procedure. When combined with diagrammatic Monte-Carlo, this method can be used to simultaneously evaluate diagrams throughout the entire $T-U-μ$ phase space of Hubbard-like models at minimal computational expense.

cond-mat.str-el↗

arXiv2018

Exchange interactions in two-state systems: rare earth pyrochlores

The general form of the nearest neighbour exchange interaction for rare earth pyrochlores is derived based on symmetry. Generally, the rare earth angular momentum degeneracy is lifted by the crystal electric field (CEF) into singlets and doublets. When the CEF ground state is a doublet that is well-separated from the first excited state the CEF ground state doublet can be treated as a pseudo-spin of some kind. The general form of the nearest neighbour exchange interaction for pseudo-spins on the pyrochlore lattice is derived for three different types of pseudo-spins. The methodology presented in this paper can be applied to other two-state spin systems with a high space group symmetry.

cond-mat.str-el↗

arXiv2014

Effective spin-1/2 exchange interactions in Tb$_2$Ti$_2$O$_7$

We derive an effective spin-1/2 exchange model for non-Kramers Tb$^{3+}$ states in the pyrochlore Tb$_2$Ti$_2$O$_7$. The four anisotropic nearest-neighbour exchange constants, as well as next-neighbour exchange constants are derived for the effective model. This work goes beyond the independent tetrahedra model by considering all nearest-neighbour exchange paths on the pyrochlore lattice. Estimates of the exchange constants reveal that Tb$_2$Ti$_2$O$_7$ is described by a quantum spin ice Hamiltonian.

cond-mat.str-el↗

arXiv2012

Magnetic order, magnetic correlations and spin dynamics in the pyrochlore antiferromagnet Er2Ti2O7

Er2Ti2O7 is believed to be a realization of an XY antiferromagnet on a frustrated lattice of corner-sharing regular tetrahedra. It is presented as an example of the order-by-disorder mechanism in which fluctuations lift the degeneracy of the ground state, leading to an ordered state. Here we report detailed measurements of the low temperature magnetic properties of Er2Ti2O7, which displays a second-order phase transition at T_N \simeq 1.2 K with coexisting short- and long-range orders. Magnetic-susceptibility studies show that there is no spin-glass-like irreversible effect. Heat-capacity measurements reveal that the paramagnetic critical exponent is typical of a 3-dimensional XY magnet while the low-temperature specific heat sets an upper limit on the possible spin-gap value and provides an estimate for the spin-wave velocity. Muon spin relaxation measurements show the presence of spin dynamics in the nanosecond time scale down to 21 mK. This time range is intermediate between the shorter time characterizing the spin dynamics in Tb2Sn2O7, which also displays long- and short-range magnetic order, and the time scale typical of conventional magnets. Hence the ground state is characterized by exotic spin dynamics. We determine the parameters of a symmetry-dictated Hamiltonian restricted to the spins in a tetrahedron, by fitting the paramagnetic diffuse neutron scattering intensity for two reciprocal lattice planes. These data are recorded in a temperature region where the assumption that the correlations are limited to nearest neighbors is fair.

cond-mat.str-el↗

arXiv2009

Unconventional superconductivity in YNi2B2C

We use the semi-classical (Doppler shift) approximation to calculate magnetic field angle-dependent density of states and thermal conductivity kappa_zz for a superconductor with a quasi-two-dimensional Fermi surface and line nodes along k_x=0 and k_y=0. The results are shown to be in good quantitative agreement with experimental results obtained for YNi2B2C.

cond-mat.supr-con↗

arXiv2008

Energetic selection of ordered states in a model of the Er2Ti2O7 frustrated pyrochlore XY antiferromagnet

We consider the possibility that the discrete long-range ordered states of Er2Ti2O7 are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchange interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er2Ti2O7, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field.

cond-mat.stat-mech↗

arXiv2008

Field angle-dependent thermal conductivity in nodal superconuctors

We apply a semi-classical method to the problem of field angle-dependent oscillations of the density of states and thermal conductivity for nodal superconductors and apply our results to the superconductor PrOs$_4$Sb$_{12}$. The oscillatory contributions to the thermal conductivity for all possible point node configurations for a superconductor with $T_h$ symmetry are calculated. It is found that experimental results are best accounted for by nodes in the off-axis directions $[\pm \sinϕ_0, 0, \pm\cosϕ_0]$, which are associated with the time-reversal breaking, triplet paired phase $D_2(E)$.

cond-mat.supr-con↗

arXiv2008

Structural distortion and the spin liquid state in Tb2Ti2O7

It is shown that a k=0, A_{2u} distortion of the terbium tetrahedral network in Tb2Ti2O7 accounts for the apparent isolation of single tetrahedra as seen in neutron scattering studies. Single tetrahedron collective spin states, rather than individual spins, account for the main features of the spin liquid state, namely, fluctuating local moments and the absence of long range order. Singlet and doublet collective spin ground states are considered. An effective interaction between tetrahedra on the fcc lattice is derived and found to be weak and anisotropic.

cond-mat.mtrl-sci↗

arXiv2007

Impurity induced density of states and residual transport in nonunitary superconductors

We obtain general expressions for the residual density of states, electrical conductivity and thermal conductivity for non-unitary superconductors due to impurity scattering. We apply the results to the so-called `B phase' of PrOs4Sb12, which we describe using a non-unitary gap function derived from symmetry considerations. The conductivity tensor has inequivalent diagonal components due to off-axis nodal positions which may be detectable in experiments.

cond-mat.supr-con↗

arXiv2007

Symmetry properties of the nodal superconductor PrOs4Sb12

We present a theoretical study of the superconducting gap function in PrOs4Sb12 using a symmetry-based approach. A three-component order parameter in the triplet channel best describes superconductivity. The gap function is non-degenerate and the lower branch has four cusp nodes at unusual points of the Fermi surface, which lead to power law behaviours in the density of states, specific heat and nuclear spin relaxation rate.

cond-mat.supr-con↗