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.
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.
I argue that Anderson's identification of the conflict between the fermi-liquid and non-fermi-liquid metallic states as the central issue of cuprate superconductivity is fundamentally wrong. 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 one 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. This implies that the central issue is actually the conflict between different kinds of order, i.e. exactly the idea implicit in Zhang's paper. I then 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. I speculate that this critical point lies on the insulating line, and that the difference between the Mott-insulator and fermi-liquid approaches to the high TC problem comes down to whether or not the superconducting states made by nand p-type doping can be continued into each other. A candidate for the second fixed point required for distinct superconducting phases is the P- and T-violating chiral spin liquid state invented by me.
This article is based on a talk by S.S. at the Nambu Memorial Symposium at the University of Chicago. We review ideas on the nature of the metallic states of the hole-doped cuprate high temperature superconductors, with an emphasis on the connections between the Luttinger theorem for the size of the Fermi surface, topological quantum field theories (TQFTs), and critical theories involving changes in the size of the Fermi surface. We begin with the derivation of the Luttinger theorem for a Fermi liquid, using momentum balance during a process of flux-insertion in a lattice electronic model with toroidal boundary conditions. We then review the TQFT of the Z2 spin liquid, and demonstrate its compatibility with the toroidal momentum balance argument. This discussion leads naturally to a simple construction of `topological' Fermi liquid states: the fractionalized Fermi liquid (FL*) and the algebraic charge liquid (ACL). We present arguments for a description of the pseudogap metal of the cuprates using Z2-FL* or Z2-ACL states with Ising-nematic order. These pseudogap metal states are also described as Higgs phases of a SU(2) gauge theory. The Higgs field represents local antiferromagnetism, but the Higgs-condensed phase does not have long-range antiferromagnetic order: the magnitude of the Higgs field determines the pseudogap, the reconstruction of the Fermi surface, and the Ising-nematic order. Finally, we discuss the route to the large Fermi surface Fermi liquid via the critical point where the Higgs condensate and Ising nematic order vanish, and the application of Higgs criticality to the strange metal.
Quantum phase transitions of metals involve changes in the Fermi surface, and can be divided into three categories. The first two categories involve symmetry breaking, and lead to a deformation or reconstruction of the Fermi surface. The third category involves a change in the volume enclosed by the Fermi surface without any symmetry breaking: one phase is a Fermi liquid (FL) with the conventional Luttinger volume, while the other phase is a `fractionalized Fermi liquid' (FL*), which has a non-Luttinger volume Fermi surface accompanied by a spin liquid with fractionalized excitations. It is a relatively simple matter to obtain a FL*-FL transition in Kondo lattice models. However, the FL*-FL transition can also be present in single-band Hubbard-like models: this is efficiently described by the `ancilla' method, which shows that the transition is a `flipped' Kondo lattice transition. This single-band FL*-FL transition is argued to apply to the metallic states of the hole-doped cuprates. In the clean limit, the critical properties of the quantum transitions in the three categories are distinct, but all lead to perfect metal transport in the quantum-critical regime. Impurity-induced `Harris disorder', with spatial fluctuations in the local position of the quantum critical point, is a relevant perturbation to the clean critical points. In the presence of Harris disorder, all three categories exhibit strange metal behavior, which can be described by a universal two-dimensional Yukawa-Sachdev-Ye-Kitaev model.
With particular reference to the role of the renormalization group (RG) approach and Ward identities (WI's), we start by recalling some old features of the one-dimensional Luttinger liquid as the prototype of non-Fermi-liquid behavior. Its dimensional crossover to the Landau normal Fermi liquid implies that a non-Fermi liquid, as, e.g., the normal phase of the cuprate high temperature superconductors, can be maintained in d>1 only in the presence of a sufficiently singular effective interaction among the charge carriers. This is the case when, nearby an instability, the interaction is mediated by critical fluctuations. We are then led to introduce the specific case of superconductivity in cuprates as an example of avoided quantum criticality. We will disentangle the fluctuations which act as mediators of singular electron–electron interaction, enlightening the possible order competing with superconductivity and a mechanism for the non-Fermi-liquid behavior of the metallic phase. This paper is not meant to be a comprehensive review. Many important contributions will not be considered. We will also avoid using extensive technicalities and making full calculations for which we refer to the original papers and to the many good available reviews. We will here only follow one line of reasoning which guided our research activity in this field.
Abstract. The normal state metallic behavior above the superconducting transition temperature (Tsc) remains one of the least understood properties since its discovery in cuprates by Bednorz and Müller [1]. Apart from the pseudogap (T ∗) phenomenon above Tsc, there is this T-linear resistivity that was first recognized by Anderson [2] as strange simply because it does not obey the low-temperature T 2 electron-electron scattering rate predicted from the Fermi liquid theory. Here, we prove that the finite temperature continu-ous quantum phase transition (CTQPT) is responsible for the transition from a strange metal to a Fermi liquid for a given chemical composition. Our proof follows the Green function formalism and the energy-level spacing renormal-ization group method. Interestingly, the CTQPT stated above can be related to the proof derived by Parameswaran, Shankar and Sondhi [3], in which, the one-to-one correspondence between the Fermi gas and Fermi liquid is indeed a special case. The theory is further exploited to give unambiguous explanations as to why and how doping gives rise to spectral weight transfer observed in the soft X-ray absorption spectroscopic measurements for the La-Sr-Cu-O system. PACS: 74.72.-h, 71.10.Hf, 74.25.F-, 74.25.Jb 1.
With particular reference to the role of the renormalization group (RG) approach and Ward identities (WI's), we start by recalling some old features of the one-dimensional Luttinger liquid as the prototype of non-Fermi-liquid behavior. Its dimensional crossover to the Landau normal Fermi liquid implies that a non-Fermi liquid, as, e.g., the normal phase of the cuprate high temperature superconductors, can be maintained in d>1 only in the presence of a sufficiently singular effective interaction among the charge carriers. This is the case when, nearby an instability, the interaction is mediated by critical fluctuations. We are then led to introduce the specific case of superconductivity in cuprates as an example of avoided quantum criticality. We will disentangle the fluctuations which act as mediators of singular electron–electron interaction, enlightening the possible order competing with superconductivity and a mechanism for the non-Fermi-liquid behavior of the metallic phase. This paper is not meant to be a comprehensive review. Many important contributions will not be considered. We will also avoid using extensive technicalities and making full calculations for which we refer to the original papers and to the many good available reviews. We will here only follow one line of reasoning which guided our research activity in this field.