Monte Carlo simulation of a many-fermion study

Ceperley, David M.; Chester, G. V.; Kalos, M. H.

doi:10.1103/physrevb.16.3081

Cited by 730 publications

(457 citation statements)

References 27 publications

Supporting

Mentioning

447

Contrasting

Order By: Relevance

Section: Gauge Theory and Variational Wave Functions For The D-wave Mmentioning

confidence: 99%

“…In both cases, the wave functions are straightforward to implement using variational Monte Carlo (VMC) methods. [31][32][33][34] For the Fermi liquid, we put the b's into a superfluid wave function ψ SF b via a typical Jastrow form, so that, schematically,is a positive wave function, the sign structure 35 of ψ FL c is identical to that of the noninteracting Fermi sea state. In contrast, 3 to model the d-metal, we put the b's into a Bose metal wave function according to the DBM construction of Refs.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Jiang

Block

Mishmash

et al. 2012

Nature

View full text Add to dashboard Cite

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's celebrated Fermi liquid theory is of central importance to many outstanding problems in condensed matter physics. Perhaps the most important such pursuit is a full microscopic characterization of the high-Tc cuprate superconductors, where the so-called "strange metal" behavior above Tc near optimal doping is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of such a strange metal quantum phase could possibly shed new light on the interesting low-temperature behavior in the pseudogap regime and on the d-wave superconductor itself. Here, we present a theory for a specific example of a strange metal, which we term the "d-wave metal." Using variational wave functions, gauge theoretic arguments, and ultimately large-scale DMRG calculations, we establish compelling evidence that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian: the venerable t-J model supplemented with a frustrated electron ring-exchange term, which we study extensively here on the two-leg ladder. These findings constitute one of the first explicit examples of a genuine non-Fermi liquid metal existing as the ground state of a realistic model.Over the past several decades, experiments on strongly correlated materials have routinely revealed, in certain parts of the phase diagram, conducting liquids with physical properties qualitatively inconsistent with Landau's Fermi liquid theory. 1 Examples of these so-called non-Fermi liquid metals 2 include the strange metal phase of the cuprate superconductors 3,4 and heavy fermion materials near a quantum critical point. 5,6 However, such non-Fermi liquid behavior has been notoriously challenging to characterize theoretically, largely owing to the failure of a weakly interacting quasiparticle description. It is even ambiguous to define a non-Fermi liquid, although possible deviations from Fermi liquid theory include, for example, violation of Luttinger's 7 famed volume theorem, vanishing quasiparticle weight, and/or anomalous thermodynamics and transport. 5,[8][9][10][11][12] This theoretical quandary is rather unfortunate as it is likely prohibiting a full understanding of the mechanism behind high-temperature superconductivity, as well as stymying theoretically-guided searches for new exotic materials.Pioneering early theoretical work on the cuprates relied on two main premises, 3,13-17 from which we will be guided but not constrained in our pursuit and understanding of a particular non-Fermi liquid metal: (1) that the microscopics can be described by the square lattice Hubbard model with on-site Coulomb repulsion, which at strong coupling reduces in its simplest form to the t-J model; and (2) that the physics of the system can be faithfully represented by the "slave-boson" technique, wherein the physical electron operator is written as a product of a slave boson ("chargon"), which carries the electronic char...

show abstract

Section: Gauge Theory and Variational Wave Functions For The D-wave Mmentioning

confidence: 99%

mentioning

confidence: 99%

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Jiang

Block

Mishmash

et al. 2012

Nature

View full text Add to dashboard Cite

show abstract

“…59 This allows for efficient evaluation of determinants and Pfaffians with rows and/or columns replaced or removed. 22,61,62 To update the inverse of an anti-symmetric matrix with a row and column replaced, we use the Sherman-Morrison algorithm 63 twice, followed by anti-symmetrization of the matrix.…”

Section: Appendix B: Fermionic Wave Functionsmentioning

confidence: 99%

“…22,59 This works as follows: Let |ψ be the wave function and let O be the observable we want to evaluate. Let {|α } be an "Ising" basis of the Hilbert space, i.e., |α is product of local basis states.…”

Section: Appendix A: Variational Monte Carlomentioning

confidence: 99%

Paired chiral spin liquid with a Fermi surface inS=1model on the triangular lattice

et al. 2012

View full text Add to dashboard Cite

Motivated by recent experiments on Ba3NiSb2O9, we investigate possible quantum spin liquid ground states for spin S = 1 Heisenberg models on the triangular lattice. We use Variational Monte Carlo techniques to calculate the energies of microscopic spin liquid wave functions where spin is represented by three flavors of fermionic spinon operators. These energies are compared with the energies of various competing three-sublattice ordered states. Our approach shows that the antiferromagnetic Heisenberg model with biquadratic term and single-ion anisotropy does not have a low-temperature spin liquid phase. However, for an SU (3)-invariant model with sufficiently strong ring-exchange terms, we find a paired chiral quantum spin liquid with a Fermi surface of deconfined spinons that is stable against all types of ordering patterns we considered. We discuss the physics of this exotic spin liquid state in relation with the recent experiment and suggest new ways to test this scenario.

show abstract

“…n σ (k) pertaining to the uniform and isotropic GSs of the Coulomb-interacting electron-gas system for d = 2 [111] (see Fig. 5.9 herein) in the low-density regime 23 and of 3 He in the normal liquid state at sufficiently large ambient pressures [105,[113][114][115][116]. In the light of this and of the strict inequality n σ (k − f;σ ) ≥ 1 2 applicable to the n σ (k) pertaining to the uniform GSs of the conventional single-band Hubbard Hamiltonian [6], employed in studies of 3 He [117][118][119], as well as to the uniform GSs of the Stoner Hamiltonian (involving contact interaction but defined on the continuum; likewise employed in studies of 3 He within the framework of the paramagnon theory [120][121][122][123][124]; for a review of spin-fluctuation theories see [125]), one observes that such Hamiltonians cannot be capable of reliably describing the normal liquid state of 3 He.…”

Section: The Case Whenmentioning

confidence: 99%

On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials inddimensions

Farid¹

2004

Philosophical Magazine

View full text Add to dashboard Cite

We demonstrate that the skeleton of the Fermi surface Sf;σ pertaining to a uniform metallic ground state (corresponding to fermions with spin index σ) is determined by the Hartree-Fock contribution Σ hf σ (k) to the dynamic self-energy Σσ(k; ε). That is to say, in order for k ∈ Sf;σ, it is necessary (but for anisotropic ground states in general not sufficient) that the following equation be satisfied:where ε k stands for the underlying non-interacting energy dispersion and εf for the exact interacting Fermi energy. The Fermi surface Sf;σ consists of the set of k points which in addition to satisfying the above equation fulfilwhereThe set of k points which satisfy the first of the above two equations but fail to satisfy the second constitute the pseudogap region of the putative Fermi surface of the interacting system. We consider the behaviour of the ground-state momentum-distribution function nσ(k) for k in the vicinity of Sf;σ and show that, whereas for the uniform metallic ground states of the conventional single-band Hubbard Hamiltonian, described in terms of an on-site interaction, nσ(k − f;σ ) ≥ 1 2 and nσ(k + f;σ ) ≤ 1 2 (here k − f;σ and k + f;σ denote vectors infinitesimally close to Sf;σ, located respectively inside and outside the underlying Fermi sea), for interactions of non-zero range these inequalities can be violated (without thereby contravening the stability condition nσ(k − f;σ ) ≥ nσ(k + f;σ )). This aspect is borne out by the nσ(k) pertaining to the normal states of for instance liquid 3 He (corresponding to a range of applied pressure) as determined by means of quantum Monte Carlo calculations. We further demonstrate that for Fermi-liquid metallic states of fermions interacting through interaction potentials of non-zero range (e.g. the Coulomb potential), the zero-temperature limit of nσ(k) does not need to be equal to 1 2 for k ∈ Sf;σ; this in strict contrast with the uniform Fermi-liquid metallic states of the single-band Hubbard Hamiltonian (if such states at all exist). This aspect should be taken into account while analyzing the nσ(k) deduced from the angle-resolved photoemission data concerning real materials. We discuss, in the light of the findings of the present work, the growing experimental evidence with regard to the 'frustration' of the kinetic energy of the charge carriers in the normal states of the copper-oxide-based high-temperature superconducting compounds.

show abstract

Monte Carlo simulation of a many-fermion study

Cited by 730 publications

References 27 publications

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Paired chiral spin liquid with a Fermi surface inS=1model on the triangular lattice

On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials inddimensions

Contact Info

Product

Resources

About