Fidelity and superconductivity in two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>t</mml:mi><mml:mtext>−</mml:mtext><mml:mi>J</mml:mi></mml:mrow></mml:math>models

Rigol, Marcos; Shastry, B. Sriram; Haas, Stephan

doi:10.1103/physrevb.80.094529

Cited by 26 publications

(35 citation statements)

References 64 publications

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“…The fidelity susceptibility provides a particularly sharp signature of the Mott phase, a result that was noted previously in the context of perodic boundary conditions and the completely connected graph [33]. Within the n th Mott lobe, χ f assumes values close to those given by second order perturbation theory [34] in the limit that t/U → 0 + :…”

Section: Quantum Measures On Ground States Of Hubbard Hamiltoniasupporting

confidence: 59%

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Mesoscopic effects in quantum phases of ultracold quantum gases in optical lattices

Carr

Wall²,

Schirmer³

et al. 2010

Phys. Rev. A

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We present a wide array of quantum measures on numerical solutions of 1D Bose-and FermiHubbard Hamiltonians for finite-size systems with open boundary conditions. Finite size effects are highly relevant to ultracold quantum gases in optical lattices, where an external trap creates smaller effective regions in the form of the celebrated "wedding cake" structure and the local density approximation is often not applicable. Specifically, for the Bose-Hubbard Hamiltonian we calculate number, quantum depletion, local von-Neumann entropy, generalized entanglement or Q-measure, fidelity, and fidelity susceptibility; for the Fermi-Hubbard Hamiltonian we also calculate the pairing correlations, magnetization, charge-density correlations, and antiferromagnetic structure factor. Our numerical method is imaginary time propagation via time-evolving block decimation. As part of our study we provide a careful comparison of canonical vs. grand canonical ensembles and Gutzwiller vs. entangled simulations. The most striking effect of finite size occurs for bosons: we observe a strong blurring of the tips of the Mott lobes accompanied by higher depletion, and show how the location of the first Mott lobe tip approaches the thermodynamic value as a function of system size.

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Section: Quantum Measures On Ground States Of Hubbard Hamiltoniasupporting

confidence: 59%

“…Fourth, we calculated both fidelity, f , and fidelity susceptibility [21,33,34], χ f . The fidelity is an overlap measure on the states, and is given by…”

Section: Models Measures and Methodsmentioning

confidence: 99%

Mesoscopic effects in quantum phases of ultracold quantum gases in optical lattices

Carr

Wall²,

Schirmer³

et al. 2010

Phys. Rev. A

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“…In the ED calculations, in order to determine ∆ c for the superconductor to Mott-insulator transition at fixed U and t , we use the ground-state fidelity metric [27][28][29][30][31][32][33] …”

Section: Resultsmentioning

confidence: 99%

Mott-insulator–to–superconductor transition in a two-dimensional superlattice

2015

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We use quantum Monte Carlo and exact diagonalization calculations to study the Mott-insulator to superconductor quantum phase transition in a two-dimensional fermionic Hubbard model with attractive interactions in the presence of a superlattice potential. The model introduced offers unique possibilities to study such transitions in optical lattice experiments. We show that, in regimes with moderate to strong interactions, the transition belongs to the 3D-XY universality class. We also explore the character of the lowest energy charge excitations in the insulating and superconducting phases and show that they can be fermionic or bosonic depending on the parameters chosen.

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“…The coupling to the Cooperon will be weak since the Fermi surface of the pockets extends only a small distance away from the nodal directions, but it will lead to a finite, but small, d -wave pairing order parameter. Recent numerical calculations using a novel fidelity approach also found evidence for such a small but finite pairing order parameter at low doping [146].…”

Section: Do Cooperons Play a Role In The Cuprates?mentioning

confidence: 93%

A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates

2011

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Abstract. The theoretical description of the anomalous properties of the pseudogap phase in the underdoped region of the cuprate phase diagram lags behind the progress in spectroscopic and other experiments. A phenomenological ansatz, based on analogies to the approach to Mott localization at weak coupling in lower dimensional systems, has been proposed by Yang, Rice and Zhang [Phys. Rev. B 73 (2006),174501]. This ansatz has had success in describing a range of experiments. The motivation underlying this ansatz is described and the comparisons to experiment are reviewed. Implications for a more microscopic theory are discussed together with the relation to theories that start directly from microscopic strongly coupled Hamiltonians.arXiv:1109.0632v1 [cond-mat.str-el]

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Fidelity and superconductivity in two-dimensionalt−Jmodels

Cited by 26 publications

References 64 publications

Mesoscopic effects in quantum phases of ultracold quantum gases in optical lattices

Mesoscopic effects in quantum phases of ultracold quantum gases in optical lattices

Mott-insulator–to–superconductor transition in a two-dimensional superlattice

A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates

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