Charge and spin structures of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi>−</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math>superconductor in the proximity of

Assaad, F. F.; Imada, Masatoshi; Scalapino, D. J.

doi:10.1103/physrevb.56.15001

Cited by 61 publications

(69 citation statements)

References 41 publications

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“…t c1 hops an electron from i ′ to j when j is vacated by an electron hopping to i. t c2 hops nearest-neighbor pairs in the same direction. Terms of this general form have been discussed in [4][5][6][7] as a mechanism for superconductivity. As we will see below, they not only favor superconductivity, but p-and d-wave density wave order as well.…”

Section: Model Hamiltoniansmentioning

confidence: 99%

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Density-wave states of nonzero angular momentum

2000

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We study the properties of states in which particle-hole pairs of non-zero angular momentum condense. These states generalize charge-and spin-density-wave states, in which s-wave particlehole pairs condense. We show that the p-wave spin-singlet state of this type has Peierls ordering, while the d-wave spin-singlet state is the staggered flux state. We discuss model Hamiltonians which favor p-wave and d-wave density wave order. There are analogous orderings for pure spin models, which generalize spin-Peierls order. The spin-triplet density wave states are accompanied by spin-1 Goldstone bosons, but these excitations do not contribute to the spin-spin correlation function. Hence, they must be detected with NQR or Raman scattering experiments. Depending on the geometry and topology of the Fermi surface, these states may admit gapless fermionic excitations. As the Fermi surface geometry is changed, these excitations disappear at a transition which is thirdorder in mean-field theory. The singlet d-wave and triplet p-wave density wave states are separated from the corresponding superconducting states by zero-temperature O(4)-symmetric critical points.

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Section: Model Hamiltoniansmentioning

confidence: 99%

“…However, they evade interactions which disfavor CDW order. Similarly, they are favored by superconductivity-favoring pair-hopping terms [4][5][6][7] while evading interactions which disfavor superconductivity. Hence, they are rather natural candidates for systems with competing repulsive interactions.…”

Section: Introductionmentioning

confidence: 99%

Density-wave states of nonzero angular momentum

2000

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“…Thus, we expect that the Hamiltonian 64, defined on the triangular lattice at half filling for a single species of (spinful) fermions, may possess an Orthogonal Metal phase at t 2 U t 1 . Such a Hamiltonian could conceivably be produced by strong electron-phonon coupling 32 .…”

Section: Realizing An Orthogonal Metalmentioning

confidence: 99%

Orthogonal metals: The simplest non-Fermi liquids

2012

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We present a fractionalized metallic phase which is indistinguishable from the Fermi liquid in conductivity and thermodynamics, but is sharply distinct in one electron properties, such as the electron spectral function. We dub this phase the 'Orthogonal Metal.' The Orthogonal Metal and the transition to it from the Fermi liquid are naturally described using a slave particle representation wherein the electron is expressed as a product of a fermion and a slave Ising spin. We emphasize that when the slave spins are disordered the result is not a Mott insulator (as erroneously assumed in the prior literature) but rather the Orthogonal Metal. We construct prototypical ground state wavefunctions for the Orthogonal Metal by modifying the Jastrow factor of Slater-Jastrow wavefunctions that describe ordinary Fermi liquids. We further demonstrate that the transition from the Fermi liquid to the Orthogonal Metal can, in some circumstances, provide a simple example of a continuous destruction of a Fermi surface with a critical Fermi surface appearing right at the critical point. We present exactly soluble models that realize an Orthogonal Metal phase, and the phase transition to the Fermi liquid. These models thus provide valuable solvable examples for phase transitions associated with the death of a Fermi surface.

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“…For a Hubbard interaction, one can for example use various forms of Hirsch's discrete HS decomposition [7,8]. For interactions taking the form of a perfect square, decompositions presented in [9] are useful. The imaginary time propagation may now be written as:…”

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Efficient calculation of imaginary-time-displaced correlation functions in the projector auxiliary-field quantum Monte Carlo algorithm

Feldbacher

Assaad

2001

Phys. Rev. B

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The calculation of imaginary time displaced correlation functions with the auxiliary field projector quantum MonteCarlo algorithm provides valuable insight (such as spin and charge gaps) in the model under consideration. One of the authors and M. Imada [1] have proposed a numerically stable method to compute those quantities. Although precise this method is expensive in CPU time. Here, we present an alternative approach which is an order of magnitude quicker, just as precise, and very simple to implement. The method is based on the observation that for a given auxiliary field the equal time Green function matrix, G, is a projector: PACS numbers: 71.27.+a, 71.10.Fd For a given Hamiltonian H = x,y c † x T x,y c y + H I and its ground state |Ψ 0 , our aim is to calculateHere, c † x creates an electron with quantum numbers x, c x (τ ) = e τ (H−µN ) c x e −τ (H−µN ) , and the chemical poten-H I corresponds to the interaction. Within the projector Quantum Monte Carlo (PQMC) algorithm, this quantity is obtained by propagating a trial wave |Ψ T function along the imaginary time axis [2-4]:The above is valid provided that: Ψ 0 |Ψ T = 0.To fix the notation, we will briefly summarize the essential steps required for the calculation of the right hand side (rhs) of the above equation at fixed values of the projection parameter Θ. A detailed review may be found in [5]. The formalism -without numerical stabilization -to compute time displaced correlation functions follows Ref.[6]. The first step is to carry out a Trotter decomposition of the imaginary time propagation: e −2ΘH = e −∆τ Ht/2 e −∆τ HI e −∆τ Ht/2 m + O((∆τ ) 2 ).Here, H t (H I ) denotes the kinetic (interaction) term of the model and m∆τ = 2Θ. Having isolated the interaction term, H I , one may carry out a Hubbard Stratonovitch (HS) transformation to obtain:where s denotes a vector of HS fields. For a Hubbard interaction, one can for example use various forms of Hirsch's discrete HS decomposition [7,8]. For interactions taking the form of a perfect square, decompositions presented in [9] are useful. The imaginary time propagation may now be written as:e −∆τ Ht/2 e x,y c † x Dx,y( sn)cy e −∆τ Ht/2 .The HS field has acquired an additional imaginary time index since we need independent fields for each time increment.The trial wave function is required to be a Slater determinant:Here N p denotes the number of particles and P is an N s × N p rectangular matrix where N s is the number of single particle states. Since U s (2Θ, 0) describes the propagation of non-interacting electrons in an external HS field, one may integrate out the fermionic degrees of freedom to obtain:where we have omitted the (∆τ ) 2 systematic error produced by the Trotter decomposition. In the above equation,

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Charge and spin structures of adx2−y2superconductor in the proximity of

Cited by 61 publications

References 41 publications

Density-wave states of nonzero angular momentum

Density-wave states of nonzero angular momentum

Orthogonal metals: The simplest non-Fermi liquids

Efficient calculation of imaginary-time-displaced correlation functions in the projector auxiliary-field quantum Monte Carlo algorithm

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