arXiv subjects

Robert M. Konik

Publications and source records attributed to Robert M. Konik.

At least 37 records · Page 2Linked to original sources

arXiv2020

Predicting impurity spectral functions using machine learning

The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral function in all of its regimes, from empty orbital, to mixed valence, to Kondo. To tackle this question, we construct two large spectral databases containing approximately 410k and 600k spectral functions of the single-channel impurity problem. We show that the NN models can accurately predict the AIM spectral function in all of its regimes, with point-wise mean absolute errors down to 0.003 in normalized units. We find that the trained NN models outperform models based on KRR and enjoy a speedup on the order of $10^5$ over traditional AIM solvers. The required size of the training set of our model can be significantly reduced using furthest point sampling in the AIM parameter space, which is important for generalizing our method to more complicated multi-channel impurity problems of relevance to predicting the properties of real materials.

cond-mat.str-el↗

arXiv2020

Probing the pathway of an ultrafast structural phase transition to illuminate the transition mechanism in Cu2S

Disentangling the primary order parameter from secondary order parameters in phase transitions is critical to the interpretation of the transition mechanisms in strongly correlated systems and quantum materials. Here we present a study of structural phase transition pathways in superionic Cu2S nanocrystals that exhibit intriguing properties. Utilizing ultrafast electron diffraction techniques sensitive in both momentum-space and the time-domain, we distinguish the dynamics of crystal symmetry breaking and lattice expansion in this system. We are able to follow the transient states along the transition pathway and so observe the dynamics of both the primary and secondary order parameters. Based on these observations we argue that the mechanism of the structural phase transition in Cu2S is dominated by the electron-phonon coupling. This mechanism advances the understanding from previous results where the focus was solely on dynamic observations of the lattice expansion.

cond-mat.str-el↗

arXiv2019

Light cone dynamics in excitonic states of two-component Bose and Fermi gases

We consider the non-equilibrium dynamics of two-component one dimensional quantum gases in the limit of extreme population imbalance where the minority species has but a single particle. We consider the situation where the gas is prepared in a state with a single spatially localized exciton: the single particle of the minority species is spatially localized while the density of the majority species in the vicinity of the minority particle sees a depression. Remarkably, we are able to consider cases where the gas contains on the order of $N=100$ particles, comparable to that studied in experiments on cold atomic gases. We are able to do by exploiting the integrability of the gas together with the observation that the excitonic state can be constructed through a simple superposition of exact eigenstates of the gas. The number of states in this superposition, rather than being exponentially large in the number of particles, scales linearly with $N$. We study the evolution of such spatially localized states in both strongly interacting Bose and Fermi gases. The behavior of the light cones when the interaction strength and density of the gas is varied can be understood from exact results for the spin excitation spectrum in these systems. We argue that the light cone in both cases exhibits scaling collapse. However unique to the Bose gas, we show that the presence of gapped finite-momentum roton-like excitations provide the Bose gas dynamics with secondary light cones.

cond-mat.quant-gas↗

arXiv2019

Signatures of rare states and thermalization in a theory with confinement

There is a dichotomy in the nonequilibrium dynamics of quantum many body systems. In the presence of integrability, expectation values of local operators equilibrate to values described by a generalized Gibbs ensemble, which retains extensive memory about the initial state of the system. On the other hand, in generic systems such expectation values relax to stationary values described by the thermal ensemble, fixed solely by the energy of the state. At the heart of understanding this dichotomy is the eigenstate thermalization hypothesis (ETH): individual eigenstates in nonintegrable systems are thermal, in the sense that expectation values agree with the thermal prediction at a temperature set by the energy of the eigenstate. In systems where ETH is violated, thermalization can be avoided. Thus establishing the range of validity of ETH is crucial in understanding whether a given quantum system thermalizes. Here we study a simple model with confinement, the quantum Ising chain with a longitudinal field, in which ETH is violated. Despite an absence of integrability, there exist rare (nonthermal) states that persist far into the spectrum. These arise as a direct consequence of confinement: pairs of particles are confined, forming new `meson' excitations whose energy can be extensive in the system size. We show that such states are nonthermal in both the continuum and in the low-energy spectrum of the corresponding lattice model. We highlight that the presence of such states within the spectrum has important consequences, with certain quenches leading to an absence of thermalization and local observables evolving anomalously.

cond-mat.str-el↗

arXiv2018

Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders

We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our work is that in practice they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications.

cond-mat.str-el↗

arXiv2018

Nonthermal states arising from confinement in one and two dimensions

We show that confinement in the quantum Ising model leads to nonthermal eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete 'meson' modes (linearly confined pairs of domain walls). These modes exist far into the spectrum and are atypical, in the sense that expectation values in the state with energy $E$ do not agree with the microcanonical (thermal) ensemble prediction. Single meson states persist above the two meson threshold, due to a surprising lack of hybridization with the ($n\geq4$)-domain wall continuum, a result that survives into the thermodynamic limit and that can be understood from analytical calculations. The presence of such states is revealed in anomalous post-quench dynamics, such as the lack of a light cone, the suppression of the growth of entanglement entropy, and the absence of thermalization for some initial states. The nonthermal states are confined to the ordered phase - the disordered (paramagnetic) phase exhibits typical thermalization patterns in both 1D and 2D in the absence of integrability.

cond-mat.stat-mech↗

arXiv2018

Quasi-local charges and the Generalized Gibbs Ensemble in the Lieb-Liniger model

We consider the construction of a generalized Gibbs ensemble composed of complete bases of conserved charges in the repulsive Lieb-Liniger model. We will show that it is possible to construct these bases with varying locality as well as demonstrating that such constructions are always possible provided one has in hand at least one complete basis set of charges. This procedure enables the construction of bases of charges that possess well defined, finite expectation values given an arbitrary initial state. We demonstrate the use of these charges in the context of two different quantum quenches: a quench where the strength of the interactions in a one-dimensional gas is switched suddenly from zero to some finite value and the release of a one dimensional cold atomic gas from a confining parabolic trap. While we focus on the Lieb-Liniger model in this paper, the principle of the construction of these charges applies to all integrable models, both in continuum and lattice form.

cond-mat.stat-mech↗

arXiv2017

Excitations in the Yang-Gaudin Bose gas

We study the excitation spectrum of two-component delta-function interacting bosons confined to a single spatial dimension, the Yang-Gaudin Bose gas. We show that there are pronounced finite-size effects in the dispersion relations of excitations, perhaps best illustrated by the spinon single particle dispersion which exhibits a gap at $2k_F$ and a finite-momentum roton minimum. Such features occur at energies far above the finite volume excitation gap, vanish slowly as $1/L$ for fixed spinon number, and can persist to the thermodynamic limit at fixed spinon density. Features such as the $2k_F$ gap also persist to multi-particle excitation continua. Our results show that excitations in the finite system can behave in a qualitatively different manner to analogous excitations in the thermodynamic limit. The Yang-Gaudin Bose gas is also host to multi-spinon bound states, known as $Λ$-strings. We study these excitations both in the thermodynamic limit under the string hypothesis and in finite size systems where string deviations are taken into account. In the zero-temperature limit we present a simple relation between the length $n$ $Λ$-string dressed energies $ε_n(λ)$ and the dressed energy $ε(k)$. We solve the Yang-Yang-Takahashi equations numerically and compare to the analytical solution obtained under the strong couple expansion, revealing that the length $n$ $Λ$-string dressed energy is Lorentzian over a wide range of real string centers $λ$ in the vicinity of $λ= 0$. We then examine the finite size effects present in the dispersion of the two-spinon bound states by numerically solving the Bethe ansatz equations with string deviations.

cond-mat.quant-gas↗

arXiv2017

Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods

We review two important non-perturbative approaches for extracting the physics of low-dimensional strongly correlated quantum systems. Firstly, we start by providing a comprehensive review of non-Abelian bosonization. This includes an introduction to the basic elements of conformal field theory as applied to systems with a current algebra, and we orient the reader by presenting a number of applications of non-Abelian bosonization to models with large symmetries. We then tie this technique into recent advances in the ability of cold atomic systems to realize complex symmetries. Secondly, we discuss truncated spectrum methods for the numerical study of systems in one and two dimensions. For one-dimensional systems we provide the reader with considerable insight into the methodology by reviewing canonical applications of the technique to the Ising model (and its variants) and the sine-Gordon model. Following this we review recent work on the development of renormalization groups, both numerical and analytical, that alleviate the effects of truncating the spectrum. Using these technologies, we consider a number of applications to one-dimensional systems: properties of carbon nanotubes, quenches in the Lieb-Liniger model, 1+1D quantum chromodynamics, as well as Landau-Ginzburg theories. In the final part we move our attention to consider truncated spectrum methods applied to two-dimensional systems. This involves combining truncated spectrum methods with matrix product state algorithms. We describe applications of this method to two-dimensional systems of free fermions and the quantum Ising model, including their non-equilibrium dynamics.

cond-mat.str-el↗

arXiv2016

Giant Spin Gap and Magnon Localization in the Disordered Heisenberg Antiferromagnet Sr2Ir1-xRuxO4

We study the evolution of magnetic excitations in the disordered two-dimensional antiferromagnet Sr2Ir1-xRuxO4. A gigantic magnetic gap greater than 40 meV opens at x = 0.27 and increases with Ru concentration, rendering the dispersive magnetic excitations in Sr2IrO4 almost momentum independent. Up to a Ru concentration of x = 0.77, both experiments and first-principles calculations show the Ir Jeff = 1/2 state remains intact. The magnetic gap arises from the local interaction anisotropy in the proximity of the Ru disorder. Under the coherent potential approximation, we reproduce the experimental magnetic excitations using the disordered Heisenberg antiferromagnetic model with suppressed next-nearest neighbor ferromagnetic coupling.

cond-mat.str-el↗

arXiv2016

Motion of a distinguishable impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking

We consider the real time dynamics of an initially localized distinguishable impurity injected into the ground state of the Lieb-Liniger model. Focusing on the case where integrability is preserved, we numerically compute the time evolution of the impurity density operator in regimes far from analytically tractable limits. We find that the injected impurity undergoes a stuttering motion as it moves and expands. For an initially stationary impurity, the interaction-driven formation of a quasibound state with a hole in the background gas leads to arrested expansion -- a period of quasistationary behavior. When the impurity is injected with a finite center of mass momentum, the impurity moves through the background gas in a snaking manner, arising from a quantum Newton's cradle-like scenario where momentum is exchanged back-and-forth between the impurity and the background gas.

cond-mat.quant-gas↗

arXiv2014

Predicting Excitonic Gaps of Semiconducting Single Walled Carbon Nanotubes From a Field Theoretic Analysis

We demonstrate that a non-perturbative framework for the treatment of the excitations of single walled carbon nanotubes based upon a field theoretic reduction is able to accurately describe experiment observations of the absolute values of excitonic energies. This theoretical framework yields a simple scaling function from which the excitonic energies can be read off. This scaling function is primarily determined by a single parameter, the charge Luttinger parameter of the tube, which is in turn a function of the tube chirality, dielectric environment, and the tube's dimensions, thus expressing disparate influences on the excitonic energies in a unified fashion. We test this theory explicitly on the data reported in NanoLetters 5, 2314 (2005) and Phys. Rev. B. 82, 195424 (2010) and so demonstrate the method works over a wide range of reported excitonic spectra.

cond-mat.str-el↗

arXiv2013

Tree tensor networks and entanglement spectra

A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, how to extract the entanglement spectra in a bipartite splitting of a loopless tensor network across multiple links of the network, by constructing a matrix product operator for the reduced density operator and simulating its eigenstates. The entanglement spectra of 2 x L, 3 x L and 4 x L with either open or periodic boundary conditions on the rungs are studied using the presented methods, where it is found that the entanglement spectrum depends not only on the subsystem but also on the boundaries between the subsystems.

cond-mat.str-el↗

arXiv2013

Constructing the generalized Gibbs ensemble after a quantum quench

Using a numerical renormalization group based on exploiting an underlying exactly solvable non- relativistic theory, we study the out-of-equilibrium dynamics of a 1D Bose gas (as described by the Lieb-Liniger model) released from a parabolic trap. Our method allows us to track the post-quench dynamics of the gas all the way to infinite time. We also exhibit a general construction, applicable to all integrable models, of the thermodynamic ensemble that has been suggested to govern this dynamics, the generalized Gibbs ensemble. We compare the predictions of equilibration from this ensemble against the long time dynamics observed using our method.

cond-mat.quant-gas↗

arXiv2010

Exciton Hierarchies in Gapped Carbon Nanotubes

We present evidence that the strong electron-electron interactions in gapped carbon nanotubes lead to finite hierarchies of excitons within a given nanotube subband. We study these hierarchies by employing a field theoretic reduction of the gapped carbon nanotube permitting electron-electron interactions to be treated exactly. We analyze this reduction by employing a Wilsonian-like numerical renormalization group. We are so able to determine the gap ratios of the one-photon excitons as a function of the effective strength of interactions. We also determine within the same subband the gaps of the two-photon excitons, the single particle gaps, as well as a subset of the dark excitons. The strong electron-electron interactions in addition lead to strongly renormalized dispersion relations where the consequences of spin-charge separation can be readily observed.

cond-mat.mes-hall↗

arXiv2007

Finite-temperature lineshapes in gapped quantum spin chains

We consider the finite-temperature dynamical structure factor (DSF) of gapped quantum spin chains such as the spin one Heisenberg model and the transverse field Ising model in the disordered phase. At zero temperature the DSF in these models is dominated by a delta-function line arising from the coherent propagation of single particle modes. Using methods of integrable quantum field theory we determine the evolution of the lineshape at low temperatures. We show that the line shape is in general asymmetric in energy and becomes Lorentzian only at temperatures far below the gap. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl_3 and YBaNiO_5.

cond-mat.str-el↗

arXiv2007

A Renormalization Group For Treating 2D Coupled Arrays of Continuum 1D Systems

We study the spectrum of two dimensional coupled arrays of continuum one-dimensional systems by wedding a density matrix renormalization group procedure to a renormalization group improved truncated spectrum approach. To illustrate the approach we study the spectrum of large arrays of coupled quantum Ising chains. We demonstrate explicitly that the method can treat the various regimes of chains, in particular the three dimensional Ising ordering transition the chains undergo as a function of interchain coupling.

cond-mat.str-el↗

arXiv2007

Transport Properties of Multiple Quantum Dots Arranged in Parallel: Results from the Bethe Ansatz

In this paper we analyze transport through a double dot system connected to two external leads. Imagining each dot possessing a single active level, we model the system through a generalization of the Anderson model. We argue that this model is exactly solvable when certain constraints are placed upon the dot Coulomb charging energy, the dot-lead hybridization, and the value of the applied gate voltage. Using this exact solvability, we access the zero temperature linear response conductance both in and out of the presence of a Zeeman field. We are also able to study the finite temperature linear response conductance. We focus on universal behaviour and identify three primary features in the transport of the dots: i) a so-called RKKY Kondo effect; ii) a standard Kondo effect; and iii) interference phenomena leading to sharp variations in the conductance including conductance zeros. We are able to use the exact solvability of the dot model to characterize these phenomena quantitatively. While here we primarily consider a double dot system, the approach adopted applies equally well to N-dot systems.

cond-mat.mes-hall↗