Strongly-correlated Systems Research Articles

On the Appearance of Families of Efimov States in the Spinor Three-Body Problem

Few-body systems with access to multiple internal levels exhibit richness beyond that typically found in their single-level counterparts. One example is that of Efimov states in strongly-correlated spinor three-body systems. In [V. E. Colussi, C. H. Greene, and J. P. D'Incao, Phys. Rev. Lett. {\bf 113}, 045302 (2014)] this problem was analyzed for spinor condensates finding a complex level structure as in an early work [Bulgac and Efimov, Sov. J. Nucl. Phys. 22, 153 (1976)] in nuclear physics, and the impact of Efimov physics on the general form of the scattering observables was worked out. In this paper we discuss the appearance of novel families of Efimov states in the spinor three-body problem.

Excitations and the tangent space of projected entangled-pair states

We develop tangent space methods for projected entangled-pair states (PEPS) that provide direct access to the low-energy sector of strongly-correlated two-dimensional quantum systems. More specifically, we construct a variational ansatz for elementary excitations on top of PEPS ground states that allows for computing gaps, dispersion relations, and spectral weights directly in the thermodynamic limit. Solving the corresponding variational problem requires the evaluation of momentum transformed two-point and three-point correlation functions on a PEPS background, which we can compute efficiently by using a contraction scheme. As an application we study the spectral properties of the magnons of the Affleck-Kennedy-Lieb-Tasaki model on the square lattice and the anyonic excitations in a perturbed version of Kitaev's toric code.

Resonating valence bond quantum Monte Carlo: Application to the ozone molecule

We study the potential energy surface of the ozone molecule by means of Quantum Monte Carlo simulations based on the resonating valence bond concept. The trial wave function consists of an antisymmetrized geminal power arranged in a single-determinant that is multiplied by a Jastrow correlation factor. Whereas the determinantal part incorporates static correlation effects, the augmented real-space correlation factor accounts for the dynamics electron correlation. The accuracy of this approach is demonstrated by computing the potential energy surface for the ozone molecule in three vibrational states: symmetric, asymmetric and scissoring. We find that the employed wave function provides a detailed description of rather strongly-correlated multi-reference systems, which is in quantitative agreement with experiment.

Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution

For the simulation of equilibrium states and finite-temperature response functions of strongly-correlated quantum many-body systems, we compare the efficiencies of two different approaches in the framework of the density matrix renormalization group (DMRG). The first is based on matrix product purifications. The second, more recent one, is based on so-called minimally entangled typical thermal states (METTS). For the latter, we highlight the interplay of statistical and DMRG truncation errors, discuss the use of self-averaging effects, and describe schemes for the computation of response functions. For critical as well as gapped phases of the spin-1/2 XXZ chain and the one-dimensional Bose-Hubbard model, we assess the computation costs and accuracies of the two methods at different temperatures. For almost all considered cases, we find that, for the same computation cost, purifications yield more accurate results than METTS -- often by orders of magnitude. The METTS algorithm becomes more efficient only for temperatures well below the system's energy gap. The exponential growth of the computation cost in the evaluation of response functions limits the attainable timescales in both methods and we find that in this regard, METTS do not outperform purifications.

Sarma phase in relativistic and non-relativistic systems

We investigate the stability of the Sarma phase in two-component fermion systems in three spatial dimensions. For this purpose we compare strongly-correlated systems with either relativistic or non-relativistic dispersion relation: relativistic quarks and mesons at finite isospin density and spin-imbalanced ultracold Fermi gases. Using a Functional Renormalization Group approach, we resolve fluctuation effects onto the corresponding phase diagrams beyond the mean-field approximation. We find that fluctuations induce a second-order phase transition at zero temperature, and thus a Sarma phase, in the relativistic setup for large isospin chemical potential. This motivates the investigation of the cold atoms setup with comparable mean-field phase structure, where the Sarma phase could then be realized in experiment. However, for the non-relativistic system we find the stability region of the Sarma phase to be smaller than the one predicted from mean-field theory. It is limited to the BEC side of the phase diagram, and the unitary Fermi gas does not support a Sarma phase at zero temperature. Finally, we propose an ultracold quantum gas with four fermion species that has a good chance to realize a zero-temperature Sarma phase.

Lattice gauge theory for condensed matter physics: ferromagnetic superconductivity as its example

Recent theoretical studies of various strongly-correlated systems in condensed matter physics reveal that the lattice gauge theory (LGT) developed in high-energy physics is quite a useful tool to understand physics of these systems. Knowledge of LGT is to become a necessary item even for condensed matter physicists. In the first part of this paper, we present a concise review of LGT for the reader who wants to understand its basics for the first time. For illustration, we choose the Abelian Higgs model, a typical and quite useful LGT, which is the lattice version of the Ginzburg–Landau model interacting with a U(1) gauge field (vector potential). In the second part, we present an account of the recent progress in the study of ferromagnetic superconductivity (SC) as an example of application of LGT to topics in condensed matter physics. As the ferromagnetism (FM) and SC are competing orders with each other, large fluctuations are expected to take place and therefore nonperturbative methods are required for theoretical investigation. After we introduce a LGT describing the FMSC, we study its phase diagram and topological excitations (vortices of Cooper pairs) by Monte Carlo simulations.

Direct observation of dynamic charge stripes in La2–xSrxNiO4

The insulator-to-metal transition continues to be a challenging subject, especially when electronic correlations are strong. In layered compounds, such as La2-xSrxNiO4 and La2-xBaxCuO4, the doped charge carriers can segregate into periodically spaced charge stripes separating narrow domains of antiferromagnetic order. Although there have been theoretical proposals of dynamically fluctuating stripes, direct spectroscopic evidence of charge-stripe fluctuations has been lacking. Here we report the detection of critical lattice fluctuations, driven by charge-stripe correlations, in La2-xSrxNiO4 using inelastic neutron scattering. This scattering is detected at large momentum transfers where the magnetic form factor suppresses the spin fluctuation signal. The lattice fluctuations associated with the dynamic charge stripes are narrow in q and broad in energy. They are strongest near the charge-stripe melting temperature. Our results open the way towards the quantitative theory of dynamic stripes and for directly detecting dynamical charge stripes in other strongly correlated systems, including high-temperature superconductors such as La2-xSrxCuO4.

Kondo Memory in Driven Strongly Correlated Quantum Dots

We investigate the real-time current response of strongly correlated quantum dot systems under sinusoidal driving voltages. By means of an accurate hierarchical equations of motion approach, we demonstrate the presence of prominent memory effects induced by the Kondo resonance on the real-time current response. These memory effects appear as distinctive hysteresis line shapes and self-crossing features in the dynamic current-voltage characteristics, with concomitant excitation of odd-number overtones. They emerge as a cooperative effect of quantum coherence-due to inductive behavior-and electron correlations-due to the Kondo resonance. We also show the suppression of memory effects and the transition to classical behavior as a function of temperature. All these phenomena can be observed in experiments and may lead to novel quantum memory applications.

A large-scale quantum simulator on a diamond surface at room temperature

Strongly-correlated quantum many-body systems exhibits a variety of exotic phases with long-range quantum correlations, such as spin liquids and supersolids. Despite the rapid increase in computational power of modern computers, the numerical simulation of these complex systems becomes intractable even for a few dozens of particles. Feynman's idea of quantum simulators offers an innovative way to bypass this computational barrier. However, the proposed realizations of such devices either require very low temperatures (ultracold gases in optical lattices, trapped ions, superconducting devices) and considerable technological effort, or are extremely hard to scale in practice (NMR, linear optics). In this work, we propose a new architecture for a scalable quantum simulator that can operate at room temperature. It consists of strongly-interacting nuclear spins attached to the diamond surface by its direct chemical treatment, or by means of a functionalized graphene sheet. The initialization, control and read-out of this quantum simulator can be accomplished with nitrogen-vacancy centers implanted in diamond. The system can be engineered to simulate a wide variety of interesting strongly-correlated models with long-range dipole-dipole interactions. Due to the superior coherence time of nuclear spins and nitrogen-vacancy centers in diamond, our proposal offers new opportunities towards large-scale quantum simulation at room temperatures.

Fluctuation Metrology Based on the Prony's Spectroscopy (II)

The basic purpose of this paper is related to creation of the basis of new metrology based on quantitative analysis of the Prony’s spectra. The Prony’s spectroscopy gives a possibility to transform a wide class of multi-periodic and random signals (associated with a clearly expressed trend) to their amplitudefrequency response (AFR). For the strongly-correlated complex systems with memory the corresponding AFR is generated by a few initial frequencies that allow realizing the further compression of the initial random signal and reading it in terms of the limited number of quantitative parameters. This important peculiarity of the Prony’s spectroscopy allows in creating of a “universal” language for reading of different fluctuations and comparing them with each other. One interesting example of reading of the infinite sequences that are formed from the transcendental numbers (the Euler’s constant E = 2.71828... and number π = 3.14159...) is considered. The new elements that are added to calculation scheme/algorithm increase the stability and accuracy of the Prony’s spectra considered. In general, it opens new possibilities in creation of the basis of the fluctuation metrology that enables to read a wide class of random signals and compare them with other signals in terms of the quantitative parameters entering into the corresponding AFRs that, in turn, are governed by the corresponding distribution of frequencies.

Is it Possible to Replace the Probability Distribution Function Describing a Random Process by the Prony’s Spectrum? (I)

The new law that governs by the generation of frequencies ωk (k=1,2,...,K-1)for the strongly-correlated systems (having a memory) has been found. The generalization of the present idea is based on detailed analysis of the previous results obtained in paper [1] that were devoted to new solutions of the Prony’s problem. It was turned out that many complex systems with memory generate new set of frequencies based on frequencies that have been generated in the nearest past. For justification of this relationship we collected different data that confirm this statement. We created also a special mathematical program, which selects (based on some criteria) a desired hypothesis that is chosen from other six similar ones. For all available data considered there is an optimal hypothesis that describes the distribution of frequencies that follows from the recurrence relationship including in itself the neighboring frequencies. The found hypothesis provides the optimal fit of the random smoothed sequence with high accuracy (the relative error less that 10%) including also the fit of the remnant function.The physical interpretation of this law is given also. This “unexpected” discovery found for a wide class of the strongly-correlated systems with memory allows to replace the probability distribution function associated with some process by its Prony’s spectrum. From mathematical point of view it will help to obtain new solutions of the old Prony’s problem and replace also the Fourier spectrum containing usually the excess of artifact frequencies by the informative-significant band of frequencies obtained from new general law that, in turn, was found for the strongly-correlated systems.

Disorder-induced zero-bias anomaly in the Anderson-Hubbard model: Numerical and analytical calculations

Using a combination of numerical and analytical calculations, we study the disorder-induced zero bias anomaly (ZBA) in the density of states of strongly-correlated systems modeled by the two dimensional Anderson-Hubbard model. We find that the ZBA comes from the response of the nonlocal inelastic self-energy to the disorder potential, a result which has implications for theoretical approaches that retain only the local self-energy. Using an approximate analytic form for the self-energy, we derive an expression for the density of states of the two-site Anderson-Hubbard model. Our formalism reproduces the essential features of the ZBA, namely that the width is proportional to the hopping amplitude $t$ and is independent of the interaction strength and disorder potential.

Revealing the high-energy electronic excitations underlying the onset of high-temperature superconductivity in cuprates

In strongly correlated systems the electronic properties at the Fermi energy (EF) are intertwined with those at high-energy scales. One of the pivotal challenges in the field of high-temperature superconductivity (HTSC) is to understand whether and how the high-energy scale physics associated with Mott-like excitations (|E−EF|>1 eV) is involved in the condensate formation. Here, we report the interplay between the many-body high-energy CuO2 excitations at 1.5 and 2 eV, and the onset of HTSC. This is revealed by a novel optical pump-supercontinuum-probe technique that provides access to the dynamics of the dielectric function in Bi2Sr2Ca0.92Y0.08Cu2O8+δ over an extended energy range, after the photoinduced suppression of the superconducting pairing. These results unveil an unconventional mechanism at the base of HTSC both below and above the optimal hole concentration required to attain the maximum critical temperature (Tc).

Application of the linear principle for the strongly-correlated variables: Calculations of differences between spectra

In this paper the authors suggest a new method of detection of possible differences between similar near infrared (NIR) spectra based on the self-similar (fractal) property. This property is a general characteristic that belongs to a wide class of the strongly-correlated systems. As an example we take a set of NIR spectra measured for three systems: (1) glassy carbon (GC) electrodes, (2) GC electrodes affected by azobenzene (AB) substance and finally (3) films (AB-FILM). Besides the physical model that should describe the intrinsic properties of these substances we found the fitting function that follow from the linear principle for the strongly-correlated variables. This function expressed in the form of linear combination of 4 power-law functions describes with the high accuracy the integrated curves that were obtained from the averaged values of the initially measured spectra. The nine fitting parameters can be considered as the quantitative “finger prints” for detection of the differences between similar spectra. Besides this result we established the self-similar behavior of the remnant functions. In other words, the difference between the initially integrated function and its fitting function can be expressed in the form of linear combinations of periodical functions having a set of frequencies following to relationship ω( k) = ω 0 ξ k , where the initial frequency ω 0 and scaling factor ξ are determined by the eigen-coordinates method. This behavior in the NIR spectra was discovered in the first time and physical reasons of such behavior merit an additional research.

Spin-liquid and magnetic phases in the anisotropic triangular lattice: The case ofκ−(ET)2X

The two-dimensional Hubbard model on the anisotropic triangular lattice, with two different hopping amplitudes $t$ and $t^\prime$, is relevant to describe the low-energy physics of $\kappa$-(ET)$_2$X, a family of organic salts. The ground-state properties of this model are studied by using Monte Carlo techniques, on the basis of a recent definition of backflow correlations for strongly-correlated lattice systems. The results show that there is no magnetic order for reasonably large values of the electron-electron interaction $U$ and frustrating ratio $t^\prime/t = 0.85$, suitable to describe the non-magnetic compound with X=Cu$_2$(CN)$_3$. On the contrary, N\'eel order takes place for weaker frustrations, i.e., $t^\prime/t \sim 0.4 \div 0.6$, suitable for materials with X=Cu$_2$(SCN)$_2$, Cu[N(CN)$_2$]Cl, or Cu[N(CN)$_2$]Br.

Onset of magnetic order in strongly-correlated systems from ab initio electronic structure calculations: application to transition metal oxides

We describe an ab initio theory of finite temperature magnetism in strongly-correlated electron systems. The formalism is based on spin density functional theory, with a self-interaction corrected local spin density approximation (SIC-LSDA). The self-interaction correction is implemented locally, within the Kohn–Korringa–Rostoker (KKR) multiple-scattering method. Thermally induced magnetic fluctuations are treated using a mean-field ‘disordered local moment’ (DLM) approach and at no stage is there a fitting to an effective Heisenberg model. We apply the theory to the 3d transition metal oxides, where our calculations reproduce the experimental ordering tendencies, as well as the qualitative trend in ordering temperatures. We find a large insulating gap in the paramagnetic state which hardly changes with the onset of magnetic order.

Magnetic monopoles in spin ice

Electrically charged particles, such as the electron, are ubiquitous. In contrast, no elementary particles with a net magnetic charge have ever been observed, despite intensive and prolonged searches (see ref. 1 for example). We pursue an alternative strategy, namely that of realizing them not as elementary but rather as emergent particles-that is, as manifestations of the correlations present in a strongly interacting many-body system. The most prominent examples of emergent quasiparticles are the ones with fractional electric charge e/3 in quantum Hall physics. Here we propose that magnetic monopoles emerge in a class of exotic magnets known collectively as spin ice: the dipole moment of the underlying electronic degrees of freedom fractionalises into monopoles. This would account for a mysterious phase transition observed experimentally in spin ice in a magnetic field, which is a liquid-gas transition of the magnetic monopoles. These monopoles can also be detected by other means, for example, in an experiment modelled after the Stanford magnetic monopole search.

Phase separation and pseudogap in electron-doped cuprates: A variational cluster perturbation analysis

We study the quantum transition from an antiferromagnet to a superconductor in the single-band Hubbard model with parameters appropriate to describe electron- and hole-doped cuprates by means of variational cluster perturbation theory, a method appropriate to deal with strongly-correlated systems. In both cases, our results produce phase separation into a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting (SC) phase at higher doping. However, in the electron-doped case the energy scale for phase separation is an order of magnitude smaller than for hole doping. This behavior can be understood in terms of the different Fermi-surface evolution in p- and n-doped materials upon doping. We argue that this behavior can be related to the different pseudogap and SC transition scales in hole- and electron-doped materials.

Self-interaction-corrected pseudopotential scheme for magnetic and strongly-correlated systems

Local-spin-density functional calculations may be affected by severe errors when applied to the study of magnetic and strongly-correlated materials. Some of these faults can be traced back to the presence of the spurious self-interaction in the density functional. Since the application of a fully self-consistent self-interaction correction is highly demanding even for moderately large systems, we pursue a strategy of approximating the self-interaction corrected potential with a non-local, pseudopotential-like projector, first generated within the isolated atom and then updated during the self-consistent cycle in the crystal. This scheme, whose implementation is totally uncomplicated and particularly suited for the pseudopotental formalism, dramatically improves the LSDA results for a variety of compounds with a minimal increase of computing cost.

Photemission and the influence of collective excitations

The development of new capabilities in high resolution photoemission is allowing detailed studies of the role of collective many-body excitations in the decay of a photohole. This in turn provides new insights into the physics of condensed matter systems, in particular the strongly-correlated systems, which exhibit a rich variety of exotic phenomena including high Tc superconductivity.