Quantum Phase Transitions of Antiferromagnets and the Cuprate Superconductors

Sachdev, Subir

doi:10.1007/978-3-642-10449-7_1

Cited by 14 publications

(16 citation statements)

References 112 publications

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“…The success of the spin-fluctuation approach to explain both the superconducting dome and the anomalous features above it would point towards a spin-wave type QCP, but in the region of optimal doping there is no real evidence for something along that line. Others propose some hidden control parameter, driving the system off the QCP at the physically relevant values [52][53][54] . Finally, the Lifshitz transition scenario 55 , possibly supported by the stripes sometimes observed 56 , is another candidate.…”

Section: Discussionmentioning

confidence: 99%

Evolution of the superconductivity dome in the two-dimensional Hubbard model

et al. 2013

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In a recent publication [Chen et al., Phys. Rev. B 86, 165136 (2012)], we identified a line of Lifshitz transition points separating the Fermi liquid and pseudogap regions in the hole-doped two dimensional Hubbard model. Here we extend the study to further determine the superconducting transition temperature in the phase diagram. By means of large-scale dynamical cluster quantum Monte Carlo simulations, we are able to identify the evolution of the d-wave superconducting dome in the hole-dope side of the phase diagram, with next-nearest-neighbor hopping (t ′ ), chemical potential and temperature as control parameters. To obtain the superconducting transition temperature Tc, we employ two-particle measurements of the pairing susceptibilities. As t ′ goes from positive to negative values, we find the d-wave projected irreducible pairing vertex function is enhanced, and the curvature of its doping dependence changes from convex to concave, which fixes the position of the maximum superconducting temperature at the same filling (n ≈ 0.85) and constraints the dome from precisely following the Lifshitz line. We furthermore decompose the irreducible vertex function into fully irreducible, charge and spin components via the parquet equations, and consistently find that the spin component dominates the pairing vertex function in the doping range where the dome is located. Our investigations deepen the understanding of the phase diagram of the two dimensional Hubbard model, and more importantly pose new questions to the field. For example, we found as t ′ goes from positive to negative values, the curvature of the pairing strength as a function of doping changes from convex to concave, and the nature of the dominant fluctuations changes from charge degree of freedom to spin degree of freedom. The study of these issues will lead to further understanding of the phase diagram of the two dimensional Hubbard model and also the physics of the hole-doped cuprate high temperature superconductors.

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Section: Discussionmentioning

confidence: 99%

Evolution of the superconductivity dome in the two-dimensional Hubbard model

et al. 2013

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“…A superconducting transition from a specific Z 2 -FL*, corresponding to a Z 2 spin liquid with favorable energetics and Ising-nematic order on the square lattice [30,32,33], was studied in Ref. [24].…”

Section: Model Of Z 2 -Fl* With Bosonic Chargonsmentioning

confidence: 99%

Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal

Chatterjee

Sachdev

2016

Phys. Rev. B

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Doping a Mott-insulating Z 2 spin liquid can lead to a fractionalized Fermi liquid (FL*). Such a phase has several favorable features that make it a candidate for the pseudogap metal for the underdoped cuprates. We focus on a particular, simple Z 2 -FL* state which can undergo a confinement transition to a spatially uniform superconductor which is smoothly connected to the "plain vanilla" BCS superconductor with d-wave pairing. Such a transition occurs by the condensation of bosonic particles carrying +e charge but no spin ("chargons"). We show that modifying the dispersion of the bosonic chargons can lead to confinement transitions with charge density waves and pair density waves at the same wave vector K, coexisting with d-wave superconductivity. We also compute the evolution of the Hall number in the normal state during the transition from the plain vanilla FL* state to a Fermi liquid, and argue, following Coleman, Marston, and Schofield [Phys. Rev. B 72, 245111 (2005)], that it exhibits a discontinuous jump near optimal doping. We note the distinction between these results and those obtained from models of the pseudogap with fermionic chargons.

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“…The Z 2 spin liquid is the simplest gapped quantum state with time-reversal symmetry and bulk anyon excitations 1-8 . For application to the cuprate superconductors, an attractive parent Mott insulating state is a Z 2 spin liquid obtained in the Schwinger boson mean field theory of the square lattice antiferromagnet with first, second, and third neighbor exchange interactions 1,9,10 . This is a fully gapped state with incommensurate spin correlations, spinon excitations which carry spin S = 1/2, vison excitations which carry Z 2 magnetic flux, and long-range Ising nematic order associated with a breaking of square lattice rotation symmetry.…”

Section: Introductionmentioning

confidence: 99%

“…It was also noted 13 that a Z 2 -FL* metal can undergo a transition into a superconducting state which is concomitant with confinement and the loss of Z 2 topological order (while preserving the Ising-nematic order). Given the recent experimental evidence for a Fermi-liquid-like metallic state in the underdoped cuprates with a density of p positively charged carriers [23][24][25] , the present paper will investigate the structure of the confining superconducting state which descends from the Z 2 -FL* state associated with Schwinger boson mean field theory of the square lattice 1, 9,10 .…”

Section: Introductionmentioning

confidence: 99%

Superconductivity from a confinement transition out of a fractionalized Fermi liquid withZ2topological and Ising-nematic orders

Chatterjee

Sachdev

et al. 2016

Phys. Rev. B

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The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped Z 2 spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the Z 2 spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the Z 2 topological and Ising-nematic orders. We describe a Higgs transition out of this deconfined metallic state into a confining superconducting state which is almost always of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation of the superconducting order. arXiv:1603.03041v2 [cond-mat.str-el] 9 Jul 2016 Acknowledgments 26 A. Derivation of the bosonic PSG 27 3 B. PSG corresponding to the nematic bosonic ansatz 28 C. Alternate derivation of the vison PSG 30 D. Derivation of the fermionic PSG 34 E. Trivial and non-trivial fusion rules 35 F. Solution for the fermionic ansatz 38 G. Alternative derivation of the specific fermionic PSG 40 H. PSG for the site bosons and constraints on H B 41 References 42

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Quantum Phase Transitions of Antiferromagnets and the Cuprate Superconductors

Cited by 14 publications

References 112 publications

Evolution of the superconductivity dome in the two-dimensional Hubbard model

Evolution of the superconductivity dome in the two-dimensional Hubbard model

Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal

Superconductivity from a confinement transition out of a fractionalized Fermi liquid withZ2topological and Ising-nematic orders

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