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arXiv:cond-mat/0610816

Quantum critical spin liquids and superconductivity in the cuprates

André LeClair

Published Oct 30, 2006• 0 citations
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Abstract

We describe a new kind of quantum critical point in the context of quantum anti-ferromagnetism in 2d that can be understood as a quantum critical spin liquid. Based on the comparison of exponents with previous numerical work, we argue it describes a transition from an anti-ferromagnetic Néel ordered state to a VBS-like state. We argue further that the symplectic fermions capture the proper degrees of freedom in the zero temperature phase that is the parent to the superconducting phase in the cuprates. We then show that our model reproduces some features found recently in experiments and also in the Hubbard model.

DOI
10.48550/arxiv.cond-mat/0610816

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We describe a new kind of quantum critical point in the context of quantum anti-ferromagnetism in 2d that can be understood as a quantum critical spin liquid. Based on the comparison of exponents with previous numerical work, we argue it describes a transition from an anti-ferromagnetic Néel ordered state to a VBS-like state. We argue further that the symplectic fermions capture the proper degrees of freedom in the zero temperature phase that is the parent to the superconducting phase in the cuprates. We then show that our model reproduces some features found recently in experiments and also in the Hubbard model.
We investigate a zero-temperature itinerant antiferromagnetic transition where the fermions possess a d-wave gap. This problem pertains to both the nodal liquid insulating phase and the d-wave superconducting phase of the underdoped cuprates. We find that a non-trivial quantum phase transition exists, and that the quantum critical point is dominated by a long-ranged interaction (∣x−y∣−2d|x-y|^{-2d}∣x−y∣−2d) of the Néel order parameter, which is induced by the Dirac-like fermions near gap nodes. We formulate a Ginzburg-Landau functional and estimate the critical exponents via the large-N expansion method.
We investigate a zero-temperature itinerant antiferromagnetic transition where the fermions possess a d-wave gap. This problem pertains to both the nodal liquid insulating phase and the d-wave superconducting phase of the underdoped cuprates. We find that a non-trivial quantum phase transition exists, and that the quantum critical point is dominated by a long-ranged interaction (|x-y|-2d) of the Néel order parameter, which is induced by the Dirac-like fermions near gap nodes. We formulate a Ginzburg–Landau functional and estimate the critical exponents via the large-n expansion method.
Soon after the discovery of high temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the "pseudogap metal" phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. We argue that the pseudogap is associated with a spin liquid, and that a particular spin liquid has the needed confining instabilities to resolve a number of open puzzles on the cuprate phase diagram.
I argue that the conflict between the fermi-liquid and non-fermi-liquid metallic states viewed by Anderson as the central intellectual issue of cuprate superconductivity, and which motivates the recent criticism by Baskaran and Anderson [cond-mat/9706076] of the work of Zhang [cond-mat/9610140], is a fundamentally wrong concept. All experimental evidence points to adiabatic continuability of the strange metal into a conventional one, and thus to one metallic phase rather than two, and all attempts to account theoretically for the existence of a luttinger-liquid at zero temperature in spatial dimension greater than 1 have failed. I discuss the underlying reasons for this failure and then argue that the true higher-dimensional generalization of the luttinger-liquid behavior is a propensity of the system to order. I speculate about how the conflict between antiferromagnetism and superconductivity, the two principal kinds of order in this problem, might result in both the observed zero-temperature phase diagram of the cuprates and the luttinger-liquid phenomenology, i.e. the breakup of the electron into spinons and holons in certain regimes of doping and energy. The key idea is a quantum critical point regulating a first-order transition between these phases and toward which one is first attracted under renormalization before bifurcating between the two phases.
Quantum spin liquids are exotic phases of quantum matter especially pertinent to many modern condensed matter systems. Dirac spin liquids (DSLs) are a class of gapless quantum spin liquids that do not have a quasi-particle description and are potentially realized in a wide variety of spin 1/2 1 / 2 magnetic systems on 2d 2 d lattices. In particular, the DSL in square lattice spin- 1/2 1 / 2 magnets is described at low energies by (2+1)d ( 2 + 1 ) d quantum electrodynamics with N_f=4 N f = 4 flavors of massless Dirac fermions minimally coupled to an emergent U(1) U ( 1 ) gauge field. The existence of a relevant, symmetry-allowed monopole perturbation renders the DSL on the square lattice intrinsically unstable. We argue that the DSL describes a stable continuous phase transition within the familiar Neel phase (or within the Valence Bond Solid (VBS) phase). In other words, the DSL is an ``unnecessary’’ quantum critical point within a single phase of matter. Our result offers a novel view of the square lattice DSL in that the critical spin liquid can exist within either the Neel or VBS state itself, and does not require leaving these conventional states.