arXiv subjects

Peter Fulde

Publications and source records attributed to Peter Fulde.

At least 19 recordsLinked to original sources

arXiv2023

Role of the action function in defining electronic wavefunctions for large systems

The dimension of the Hilbert space needed for the description of an interacting electron system increases exponentially with electron number $N$. As pointed out by W. Kohn this exponential wall problem (EWP) limits the concept of many-electron wavefunctions based on solutions of Schr\"odinger's equation to $N \leq N_0$, where $N_0 \approx 10^3$ \cite{Kohn1999}. This limitation does not hold when the electronic interactions are neglected or treated in a mean-field approximation. The EWP has directed electronic structure calculations for solids to methods like density-functional theory which avoid dealing with many-electron wavefunctions. We show that the highly unsatisfactory limitation of many-electron wavefunctions to $N \leq N_0$ can be overcome by generalizing their definition. We show for the ground state of a large system that it is the logarithm of the solution of Schr\"odinger's equation which should be used to characterize this system. In this case the wavefunctions of independent subsystems add up rather than multiply. This feature is realized by the action function. It provides a simple physical picture for the resolution of the EWP.

cond-mat.str-el↗

arXiv2018

Ground-state wavefunction of macroscopic electron systems

Wavefunctions for large electron numbers $N$ are plagued by the Exponential Wall Problem (EWP), i.e., an exponential increase in the dimensions of Hilbert space with $N$. Therefore they loose their meaning for macroscopic systems, a point stressed in particular by W. Kohn. The EWP has to be resolved in order to be able to perform electronic structure calculations, e.g., for solids. The origin of the EWP is the multiplicative property of wavefunctions when independent subsystems are considered. Therefore it can only be avoided when wavefunctions are formulated so that they are additive instead, in particular when matrix elements involving them are calculated. We describe how this is done for the ground state of a macroscopic electron system. Going over from a multiplicative to an additive quantity requires taking a logarithm. Here it implies going over from Hilbert space to the operator- or Liouville space with a metric based on cumulants. The operators which define the ground-state wavefunction generate fluctuations from a mean-field state. The latter does not suffer from an EWP and therefore may serve as a vacuum state. The fluctuations have to be {\it connected} like the ones caused by pair interactions in a classical gas when the free energy is calculated (Meyer's cluster expansion). This fixes the metric in Liouville space. The scheme presented here provides a solid basis for electronic structure calculations for the ground state of solids. In fact, its applicability has already been proven. We discuss also matrix product states, which have been applied to one-dimensional systems with results of high precision. Although these states are formulated in Hilbert space they are processed by using operators in Liouville space. We show that they fit into the general formalism described above.

cond-mat.other↗

arXiv2017

Wavefunctions for large electronic systems

Wavefunctions for large electron numbers suffer from an exponential growth of the Hilbert space which is required for their description. In fact, as pointed out by W. Kohn, for electron numbers $N > N_0$ where $N_0 \approx 10^3$ they become meaningless (exponential wall problem). Nevertheless, despite of the enormous successes of density functional theory, one would also like to develop electronic structure calculations for large systems based on wavefunctions. This is possible if one defines the latter in Liouville space with a cumulant metric rather than in Hilbert space. The cluster expansion of the free energy of a classical monoatomic gas makes it plausible that cumulants are a proper tool for electronic structure calculations.

physics.chem-ph↗

arXiv2017

Dealing with the exponential wall in electronic structure calculations

An alternative to Density Functional Theory are wavefunction based electronic structure calculations for solids. In order to perform them the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the number of configurations with increasing electron number N. There are different routes one may follow. One is to characterize a many-electron wavefunction by a vector in Liouville space with a cumulant metric rather than in Hilbert space. This removes the EW problem. Another is to model the solid by an {\it impurity} or {\it fragment} embedded in a {\it bath} which is treated at a much lower level than the former. This is the case in Density Matrix Embedding Theory (DMET) or Density Embedding Theory (DET). The latter are closely related to a Schmidt decomposition of a system and to the determination of the associated entanglement. We show here the connection between the two approaches. It turns out that the DMET (or DET) has an identical active space as a previously used Local Ansatz, based on a projection and partitioning approach. Yet, the EW problem is resolved differently in the two cases. By studying a $H_{10}$ ring these differences are analyzed with the help of the method of increments.

physics.chem-ph↗

arXiv2017

Critical magnetic field of ultrathin superconducting films and interfaces

We derive an analytic expression for the temperature dependent critical magnetic field parallel to ultrathin superconducting films with Rashba spin-orbit interaction. Thereby we cover the range from small to large spin-orbit interactions $\lambda$ compared with the gap parameter $\Delta_0$. We find that at a critical spin-orbit energy $\lambda_c$ a first-order phase transition takes place at which the pairing momentum of the Cooper pairs changes discontinuously. We speculate that this might give raise to new phenomena. With increasing $\lambda/\Delta_0$, the pair formation changes from interband to intraband pairing. For $\lambda>\lambda_c$, a dimensional cross-over of the critical field from two to one dimension is taking place.

cond-mat.supr-con↗

arXiv2016

Covalency and vibronic couplings make a nonmagnetic j=3/2 ion magnetic

For 4$d^1$ and 5$d^1$ spin-orbit-coupled electron configurations, the notion of nonmagnetic j=3/2 quartet ground state discussed in classical textbooks is at odds with the observed variety of magnetic properties. Here we throw fresh light on the electronic structure of 4$d^1$ and 5$d^1$ ions in molybdenum- and osmium-based double-perovskite systems and reveal different kinds of on-site many-body physics in the two families of compounds: while the sizable magnetic moments and $g$ factors measured experimentally are due to both metal $d$-ligand $p$ hybridization and dynamic Jahn-Teller interactions for 4$d$ electrons, it is essentially $d$-$p$ covalency for the 5$d^1$ configuration. These results highlight the subtle interplay of spin-orbit interactions, covalency and electron-lattice couplings as the major factor in deciding the nature of the magnetic ground states of 4$d$ and 5$d$ quantum materials. Cation charge imbalance in the double-perovskite structure is further shown to allow a fine tuning of the gap between the $t_{2g}$ and $e_g$ levels, an effect of much potential in the context of orbital engineering in oxide electronics.

cond-mat.str-el↗

arXiv2015

Wavefunctions for large systems as basis for electronic structure calculations

Electronic structure calculations for solids based on many-electron wavefunctions have been hampered by the argument that for large electron numbers wavefunctions are not a legitimate scientific concept, because they face an exponential wall problem. We show that this problem can be avoided by using cumulant techniques in formulating wavefunctions. Therefore calculations for solids based on many-electron functions are possible and useful. This includes also systems with strongly correlated electrons.

cond-mat.mtrl-sci↗

arXiv2014

Electron correlation effects in diamond: a wave-function quantum chemistry study of the quasiparticle band structure

The quasiparticle bands of diamond, a prototype covalent insulator, are herein studied by means of wave-function electronic-structure theory, with emphasis on the nature of the correlation hole around a bare particle. Short-range correlations are in such a system conveniently described by using a real-space representation and many-body techniques from {\it ab initio} quantum chemistry. To account for long-range polarization effects, on the other hand, we adopt the approximation of a dielectric continuum. Having as "uncorrelated" reference the Hartree-Fock band structure, the post-Hartree-Fock treatment is carried out in terms of localized Wannier functions derived from the Hartree-Fock solution. The computed correlation-induced corrections to the relevant real-space matrix elements are important and give rise to a strong reduction, in the range of $50\%$, of the initial Hartree-Fock gap. While our final results for the indirect and direct gaps, 5.4 and 6.9 eV, respectively, compare very well with the experimental data, the width of the valence band comes out by $10$ to $15\%$ too large as compared to experiment. This overestimation of the valence-band width appears to be related to size-consistency effects in the configuration-interaction correlation treatment.

cond-mat.mtrl-sci↗

arXiv2012

Topological states in pyrochlore iridates: long-range anisotropy strongly competing with spin-orbit interaction

In the search for topological phases in correlated electron systems, iridium-based pyrochlores A2Ir2O7 -- materials with 5d transition-metal ions -- provide fertile grounds. Several novel topological states have been predicted but the actual realization of such states is believed to critically depend on the strength of local potentials arising from distortions of IrO6-cages. We test this hypothesis by measuring with resonant x-ray scattering the electronic level splittings in the A= Y, Eu systems, which we show to agree very well with ab initio electronic structure calculations. We find, however, that not distortions of IrO6-octahedra are the primary source for quenching the spin-orbit interaction, but strong long-range lattice anisotropies, which inevitably break the local cubic symmetry and will thereby be decisive in determining the system's topological ground state.

cond-mat.str-el↗

arXiv2011

Ab initio calculation of d-d excitations in quasi-one-dimensional Cu d9 correlated materials

With wavefunction-based electronic-structure calculations we determine the Cu d-d excitation energies in quasi-one-dimensional spin-chain and ladder copper oxides. A complete set of local excitations has been calculated for cuprates with corner-sharing (Sr2CuO3 and SrCuO2) and edge-sharing (LiVCuO4, CuGeO3, LiCu2O2 and Li2CuO2) CuO4 plaquettes, with corner-sharing CuF6 octahedra (KCuF3), for the ladder system CaCu2O3, and for multiferroic cupric oxide CuO. Our data compare well with available results of optical absorption measurements on KCuF3 and the excitation energies found by resonant inelastic x-ray scattering experiments for CuO. The ab initio results we report for the other materials should be helpful for the interpretation of future resonant inelastic x-ray scattering experiments on those highly anisotropic compounds.

cond-mat.str-el↗

arXiv2011

Quantum Ice : a quantum Monte Carlo study

Ice states, in which frustrated interactions lead to a macroscopic ground-state degeneracy, occur in water ice, in problems of frustrated charge order on the pyrochlore lattice, and in the family of rare-earth magnets collectively known as spin ice. Of particular interest at the moment are "quantum spin ice" materials, where large quantum fluctuations may permit tunnelling between a macroscopic number of different classical ground states. Here we use zero-temperature quantum Monte Carlo simulations to show how such tunnelling can lift the degeneracy of a spin or charge ice, stabilising a unique "quantum ice" ground state --- a quantum liquid with excitations described by the Maxwell action of 3+1-dimensional quantum electrodynamics. We further identify a competing ordered "squiggle" state, and show how both squiggle and quantum ice states might be distinguished in neutron scattering experiments on a spin ice material.

cond-mat.str-el↗

arXiv2011

Extended quantum U(1)-liquid phase in a three-dimensional quantum dimer model

Recently, quantum dimer models, in which the system can tunnel between different classical dimer configurations, have attracted a great deal of interest as a paradigm for the study of exotic quantum phases. Much of this excitement has centred on the claim that a certain class of quantum dimer model, defined on a bipartite lattice, can support a quantum U(1)-liquid phase with deconfined fractional excitations in three dimensions. These fractional monomer excitations are quantum analogues of the magnetic monopoles found in spin ice. In this article we use extensive quantum Monte Carlo simulations to establish the ground-state phase diagram of the quantum dimer model on the three-dimensional, bipartite, diamond lattice as a function of the ratio {\mu} of the potential to kinetic energy terms in the Hamiltonian. We find that, for {\mu}_c = 0.75 +/- 0.04, the model undergoes a first-order quantum phase transition from an ordered "R-state" into an extended quantum U(1)-liquid phase, which terminates in a quantum critical "RK point" for {\mu}=1. This confirms the published field-theoretical scenario. We present detailed evidence for the existence of the U(1)-liquid phase, and indirect evidence for the existence of its photon and monopole excitations. We also explore some of the technical ramifications of this analysis, benchmarking quantum Monte Carlo against a variety of exact and perturbative results, comparing different variational wave functions. The ergodicity of the quantum dimer model on a diamond lattice is discussed in detail. These results complete and extend the analysis previously published in [O. Sikora et al., Phys. Rev. Lett. 103, 247001 (2009)].

cond-mat.str-el↗

arXiv2011

Fermionic quantum dimer and fully-packed loop models on the square lattice

We consider fermionic fully-packed loop and quantum dimer models which serve as effective low-energy models for strongly correlated fermions on a checkerboard lattice at half and quarter filling, respectively. We identify a large number of fluctuationless states specific to each case, due to the fermionic statistics. We discuss the symmetries and conserved quantities of the system and show that for a class of fluctuating states in the half-filling case, the fermionic sign problem can be gauged away. This claim is supported by numerical evaluation of the low-lying states and can be understood by means of an algebraic construction. The elimination of the sign problem then allows us to analyze excitations at the Rokhsar-Kivelson point of the models using the relation to the height model and its excitations, within the single-mode approximation. We then discuss a mapping to a U(1) lattice gauge theory which relates the considered low-energy model to the compact quantum electrodynamics in 2+1 dimensions. Furthermore, we point out consequences and open questions in the light of these results.

cond-mat.str-el↗

arXiv2010

Ab Initio determination of Cu 3d orbital energies in layered copper oxides

It has long been argued that the minimal model to describe the low-energy physics of the high-Tc superconducting cuprates must include copper states of other symmetries besides the canonical x2-y2 one, in particular the z2 orbital. Experimental and theoretical estimates of the energy splitting of these states vary widely. With a novel ab initio quantum chemical computational scheme we determine these energies for a range of copper-oxides and -oxyclorides, determine trends with the apical Cu-ligand distances and find excellent agreement with recent Resonant Inelastic X-ray Scattering measurements, available for La2CuO4, Sr2CuO2Cl2, and CaCuO2.

cond-mat.str-el↗

arXiv2010

Strongly correlated fermions on a kagome lattice

We study a model of strongly correlated spinless fermions on a kagome lattice at 1/3 filling, with interactions described by an extended Hubbard Hamiltonian. An effective Hamiltonian in the desired strong correlation regime is derived, from which the spectral functions are calculated by means of exact diagonalization techniques. We present our numerical results with a view to discussion of possible signatures of confinement/deconfinement of fractional charges.

cond-mat.str-el↗

arXiv2010

Metal-insulator transition of the Kagome lattice fermions at 1/3 filling

We discuss the metal-insulator transition of the spinless fermion model on the Kagom\'{e} lattice at 1/3-filling. The system is analyzed using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of the effective model with a plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping integrals, reflecting the difference of band structure at the Fermi level.

cond-mat.str-el↗

arXiv2009

Full Self-Consistent Projection Operator Approach to Nonlocal Excitations in Solids

A self-consistent projection operator method for single-particle excitations is developed. It describes the nonlocal correlations on the basis of a projection technique to the retarded Green function and the off-diagonal effective medium. The theory takes into account long-range intersite correlations making use of an incremental cluster expansion in the medium. A generalized self-consistent coherent potential is derived. It yields the momentum-dependent excitation spectra with high resolution. Numerical studies for the Hubbard model on a simple cubic lattice at half filling show that the theory is applicable in a wide range of Coulomb interaction strength. In particular, it is found that the long-range antiferromagnetic correlations in the strong interaction regime cause shadow bands in the low-energy region and sub-peaks of the Mott-Hubbard bands.

cond-mat.str-el↗

arXiv2009

Nanomechanical Detection of Itinerant Electron Spin Flip

Spin is an intrinsically quantum property, characterized by angular momentum. A change in the spin state is equivalent to a change in the angular momentum or mechanical torque. This spin-induced torque has been invoked as the intrinsic mechanism in experiments ranging from the measurements of angular momentum of photons g-factor of metals and magnetic resonance to the magnetization reversal in magnetic multi-layers A spin-polarized current introduced into a nonmagnetic nanowire produces a torque associated with the itinerant electron spin flip. Here, we report direct measurement of this mechanical torque and itinerant electron spin polarization in an integrated nanoscale torsion oscillator, which could yield new information on the itinerancy of the d-band electrons. The unprecedented torque sensitivity of 10^{-22} N m/ \sqrt{Hz} may enable applications for spintronics, precision measurements of CP-violating forces, untwisting of DNA and torque generating molecules.

cond-mat.mes-hall↗