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P. R. Crompton

Publications and source records attributed to P. R. Crompton.

17 recordsLinked to original sources
arXiv2010

Grobner Bases for Finite-temperature Quantum Computing and their Complexity

Following the recent approach of using order domains to construct Grobner bases from general projective varieties, we examine the parity and time-reversal arguments relating de Witt and Lyman's assertion that all path weights associated with homotopy in dimensions d <= 2 form a faithful representation of the fundamental group of a quantum system. We then show how the most general polynomial ring obtained for a fermionic quantum system does not, in fact, admit a faithful representation, and so give a general prescription for calcluating Grobner bases for finite temperature many-body quantum system and show that their complexity class is BQP.

quant-ph↗
arXiv2009

Nonperturbative Renormalization of the Heisenberg Spin-1/2 Antiferromagnet on the Square Lattice

We investigate the critical scaling of the spin-1/2 antiferromagnet on the square lattice in the easy-plane (XXZ) regime, via numerical measurements of the entanglement entropy constructed from the zeroes of a polynomial ring. We relate these results to conformal field theory predictions for the area law scaling of entanglement entropyin the vicinity of quantum critical points in gapless conformally invariant 2d quantum systems, and in gapless systems with finite Fermi surfaces. Our measurements are focused in three low-temperature regions at fixed XXZ anisotropies of $Δ=1.01$, $Δ=1.78$ and $Δ=2.0$ which probe the quantum regime between the Néel point and Ising phase.

cond-mat.stat-mech↗
arXiv2009

The Decoherence of the Electron Spin Polarization and Meta-stability of $C^{13}$ Nuclei in Diamond

Following the recent successful formation and manipulation of entangled $C^{13}$ atoms on the surface of Diamond we calculate the decoherence of the electron spin polarization in Diamond via a nonperturbative treatment of the time-dependent Greens function of the Central-Spin model, describing the phonon and Hyperfine couplings of the electron to a bath of $C^{13}$ atoms, for arbitrary initial polarizations, applied field strengths, and for up to eight entangled $C^{13}$ atoms. We compare these numerical results with the exact treatment available in the fully initially polarized limit of the non-Markovian dynamics regime, and comment on the role of dangerously irrelevant scaling in the meta-stability of $C^{13}$ flip-flop processes.

cond-mat.mes-hall↗
arXiv2009

The Quantum Noise of Ferromagnetic $π$-Bloch Domain Walls

We quantify the probability per unit Euclidean-time of reversing the magnetization of a $π$-Bloch vector, which describes the Ferromagnetic Domain Walls of a Ferromagnetic Nanowire at finite-temperatures, by evaluating the saddlepoint solution of the grand canonical partition function for the Ferromagnetic Nanowire consisting of $N$ such soliton and anti-soliton states. Our approach, based on Langer's Theory, treats the double Sine-Gordon model that defines the $π$-Bloch vectors via a procedure of nonperturbative renormalization, and uses importance sampling methods to minimise the free energy of the system, and identify the saddlepoint solution corresponding to the reversal probability. We identify that whilst the general solution for the free energy minima cannot be expressed in closed form, we can obtain a closed expression for the saddlepoint by maximizing the entanglement entropy of the system. We use this approach to quantify the geometric and non-geometric contributions to the entanglement entropy of the Ferromagnetic Nanowire, defined between entangled Ferromagnetic Domain Walls, and evaluate the Euclidean-time dependence of the domain wall width and angular momentum transfer at the domain walls, which has been recently proposed as a mechanism for Quantum Memory Storage.

cond-mat.mes-hall↗
arXiv2008

The Partition Function Zeroes of Quantum Critical Points

The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity $e^{hΔτ}$, and the Euclidean-time lattice spacing $Δτ$ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as parity. We now present a first numerical analysis for this new zeros approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, $c$, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.

cond-mat.stat-mech↗
arXiv2008

Lorentz Covariance and the Dimensional Crossover of 2d-Antiferromagnets

We derive a lattice $β$-function for the 2d-Antiferromagnetic Heisenberg model, which allows the lattice interaction couplings of the nonperturbative Quantum Monte Carlo vacuum to be related directly to the zero-temperature fixed points of the nonlinear sigma model in the presence of strong interplanar and spin anisotropies. In addition to the usual renormalization of the gapful disordered state in the vicinity of the quantum critical point, we show that this leads to a chiral doubling of the spectra of excited states.

cond-mat.mes-hall↗
arXiv2006

The Lattice $β$-function of Quantum Spin Chains

We derive the lattice $β$-function for quantum spin chains, suitable for relating finite temperature Monte Carlo data to the zero temperature fixed points of the continuum nonlinear sigma model. Our main result is that the asymptotic freedom of this lattice $β$-function is responsible for the nonintegrable singularity in $θ$, that prevents analytic continuation between $θ=0$ and $θ=π$.

hep-th↗
arXiv2006

Leading Corrections to Finite-Size Scaling for Mixed-spin Chains

We identify the leading corrections to Finite-Size Scaling relations for the correlation length and twist order parameter of three mixed-spin quantum spin chains for the critical feature that develops at, $θ=π$, corresponding to a change in the topological realisation of the groundstates.

cond-mat.str-el↗
arXiv2006

Exact Nonperturbative Renormalization

We propose an exact renormalization group equation for Lattice Gauge Theories, that has no dependence on the lattice spacing. We instead relate the lattice spacing properties directly to the continuum convergence of the support of each local plaquette. Equivalently, this is formulated as a convergence prescription for a characteristic polynomial in the gauge coupling that allows the exact meromorphic continuation of a nonperturbative system arbitrarily close to the continuum limit.

hep-lat↗
arXiv2005

Spontaneous Parity Violation

We disprove the Vafa-Witten theorem on the impossibility of spontaneously breaking parity in vector-like gauge field theories, identifying a mechanism driven by quantum fluctuations. With the introduction of a meromorphic Lattice formulation, defined over 5 dimensions, we demonstrate that the minima of the free energy can be distinct from the maxima of the partition function : identifying and evaluating a suitable contour for the partition function defined such that asymptotic behaviour of the complex action is non-oscillatory.

hep-lat↗
arXiv2005

Asymptotics of the Infrared

We follow recent formulations of dimensionally reduced loop operators for quantum field theories and exact representations of probabilistic lattice dynamics to identify a new scheme for the evaluation of partition function zeroes, allowing for the explicit analysis of quantum critical phenomena. This new approach gives partition function zeroes from a factored quantum loop operator basis and, as we show, constitutes an effective mapping of the renormalization group $β$-function onto the noncommuting local operator basis of a countably finite Hilbert space. The Vafa-Witten theorem for CP-violation and related complex action problems of Euclidean Field theories are discussed, following recent treatments, and are shown to be natural consequences of the analyticity of the limiting distribution of these zeroes, and properties of vacuum regimes governed by a dominant quantum fluctuation in the vicinity of a renormalization group equation fixed point in the infrared.

hep-lat↗
arXiv2004

Finite Size Scaling, Fisher Zeroes and N=4 Super Yang-Mills

We investigate critical slowing down in the local updating continuous-time Quantum Monte Carlo method by relating the finite size scaling of Fisher Zeroes to the dynamically generated gap, through the scaling of their respective critical exponents. As we comment, the nonlinear sigma model representation derived through the hamiltonian of our lattice spin model can also be used to give a effective treatment of planar anomalous dimensions in N=4 SYM. We present scaling arguments from our FSS analysis to discuss quantum corrections and recent 2-loop results, and further comment on the prospects of extending this approach for calculating higher twist parton distributions.

hep-lat↗
arXiv2003

Interpolating the Free Energy Density Differences of Reweighting Methods

A discussion of the overlap problem of reweighting approaches to evaluating critical phenomenon in fermionic systems is motivated by highlighting the divergence of the joint probability density function of a general ratio. By identifying the bounds for which this integral can be expressed in closed form, we establish criteria for accurately mapping the joint ratio distribution of two disjoint ensembles through interpolation. The approach is applied to QCD with four staggered flavours to evaluate the critical line in the $β-μ$ plane.

hep-lat↗
arXiv2002

Composite reweighting with Imaginary Chemical Potentials in SU(3)

We review the overlap pathology of the Glasgow reweighting method for finite density QCD, and discuss the sampling bias that effects the determination of the ensemble-averaged fugacity polynomial expansion coefficients that form the Grand Canonical Partition function. The expectation of the difference in free energies between canonical partition functions generated with different measures is presented as an indicator of a systematic quark number dependent biasing in the reweighting approach. The advantages of building up an unbiased polynomial expansion for the Grand Canonical Partition function through a series of parallel ensembles generated by reweighting with imaginary chemical potentials are then contrasted with addressing the overlap pathology through a secondary reweighting.

hep-lat↗
arXiv2001

Composite reweighting SU(2) QCD at Finite Temperature

The Glasgow reweighting method is evaluated for SU(2) lattice gauge theory at nonzero μand finite T. We establish that the ' overlap problem' of SU(3) measurements, in which the transition points determined from thermodynamic observables have an unphysical dependence on the value of μused in the reweighting persists for SU(2). By combining the information from different lattice ensembles we alleviate sampling bias in the fugacity expansion, and identify the Lee-Yang zeros associated with the transition to a high density phase that can plausibly be associated with diquark condensation. We also confirm the existence of a line of first order transitions above a critical point in the T-μplane previously identified by effective chiral lagrangian calculations.

hep-lat↗
arXiv2001

Composite Reweighting the Glasgow Method for Finite Density QCD

The reweighting method developed in Glasgow to circumvent the lattice action becoming complex at finite density suffers from a pathological onset transition thought to be due to the reweighting. We present a new reweighting scheme based on this approach in which we combine ensembles to alleviate the sampling bias we identify in the polynomial coefficients of the fugacity expansion.

hep-lat↗