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arXiv:cond-mat/0003163 · Physical review. B, Condensed matter

Competing orders and quantum criticality in doped antiferromagnets

Matthias Vojta C, Ying Zhang, Subir Sachdev A

Published Sep 1, 2000• 150 citations
arXivHTMLPDF

Abstract

We use a number of large-N limits to explore the competition between ground states of square lattice doped antiferromagnets which break electromagnetic $U(1),$ time-reversal, or square lattice space-group symmetries. Among the states we find are d-, ${(s}^{*}+id)\ensuremath{-},$ and ${(d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}})$-wave superconductors, Wigner crystals, Wigner crystals of hole pairs, orbital antiferromagnets (or staggered-flux states), and states with spin-Peierls and bond-centered charge stripe order. In the vicinity of second-order quantum phase transitions between the states, we go beyond the large-N limit by identifying the universal quantum field theories for the critical points, and computing the finite temperature, quantum critical damping of fermion spectral functions. We identify candidate critical points for the recently observed quantum critical behavior in photoemission experiments on ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Ca}\mathrm{}\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ by Valla et al. [Science 285, 2110 (1999)]. These involve onset of a charge-density wave, or of broken time-reversal symmetry with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}}$ or ${s}^{*}+id$ pairing, in a d-wave superconductor. It is not required (although it is allowed) that the stable state in the doped cuprates be anything other than the d-wave superconductor---the other states need only be stable nearby in parameter space. At finite temperatures, fluctuations associated with these nearby states lead to the observed fermion damping in the vicinity of the nodal points in the Brillouin zone. The cases with broken time-reversal symmetry are appealing because the order parameter is not required to satisfy any special commensurability conditions. The observed absence of inelastic damping of quasiparticles with momenta $(\ensuremath{\pi},k),$ $(k,\ensuremath{\pi})$ (with $0<~k<~\ensuremath{\pi})$ also appears very naturally for the case of fluctuations to ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}}$ order.

DOI
10.1103/physrevb.62.6721

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We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory of N f = 2 massless Dirac fermions carrying fundamental gauge charges—this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice with π -flux per plaquette in the ℤ 2 center of SU(2). This theory has an emergent SO(5) f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ 2 -flux. At half-filling, the low-energy theory of the Higgs sector has N b = 2 relativistic bosons with a possible emergent SO(5) b global symmetry describing rotations between a d -wave superconductor, period-2 charge stripes, and the time-reversal breaking “ d -density wave” state. We propose a conformal SU(2) gauge theory with N f = 2 fundamental fermions, N b = 2 fundamental bosons, and a SO(5) f ×SO(5) b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5) f and a confining state which breaks SO(5) b . The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and d -wave superconductivity. A similar theory applies at nonzero doping and large U , with longer-range couplings of the chargons leading to charge order with longer periods.
Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step toward a quantitative theory of the competition between antiferromagnetism and ddd-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The ddd-wave order parameter is found to scale like the superexchange coupling JJJ for on-site interaction UUU comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping, while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second neighbor hopping ${t}^{\ensuremath{'}}$, the zero-temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third neighbor hopping ${t}^{\ensuremath{''}}$ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs Tc∕Tcmax{T}_{c}∕{T}_{c}^{\mathit{max}}Tc​∕Tcmax​ phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of ddd-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling, ddd-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.
We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order |∆|, where ∆ is pairing amplitude, so that the region of SDW order is smaller in the superconductor than in the metal. This shift is larger than the |∆|2 shift predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by copper based high temperature superconductors. Based on spin and charge fractionalization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductivity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractionalization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as “nodal-antinodal dichotomy” at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such universal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs.
The square-lattice Hubbard and closely related t-J models are considered as basic paradigms for understanding strong correlation effects and unconventional superconductivity (SC). Recent large-scale density matrix renormalization group simulations on the extended t-J model have identified d-wave SC on the electron-doped side (with the next-nearest-neighbor hopping t_{2}>0) but a dominant charge density wave (CDW) order on the hole-doped side (t_{2}<0), which is inconsistent with the SC of hole-doped cuprate compounds. We re-examine the ground-state phase diagram of the extended t-J model by employing the state-of-the-art density matrix renormalization group calculations with much enhanced bond dimensions, allowing more accurate determination of the ground state. On six-leg cylinders, while different CDW phases are identified on the hole-doped side for the doping range δ=1/16-1/8, a SC phase emerges at a lower doping regime, with algebraically decaying pairing correlations and d-wave symmetry. On the wider eight-leg systems, the d-wave SC also emerges on the hole-doped side at the optimal 1/8 doping, demonstrating the winning of SC over CDW by increasing the system width. Our results not only suggest a new path to SC in general t-J model through weakening the competing charge orders, but also provide a unified understanding on the SC of both hole- and electron-doped cuprate superconductors.
Abstract We present a T = 0 K renormalization group (RG) phase diagram for the hole-doped 2D Hubbard model on the square lattice. The RG method employed is nonperturbative in treating quantum fluctuations of the single-particle occupation number via the unitarily decoupling of one electronic state at every RG step. As a result, the RG phase diagram possesses the quantum fluctuation energy scale (ω) as one of its axes. Using effective Hamiltonians and wavefunctions for the low-energy many-body eigenstates for the doped Mott liquid obtained from the stable fixed point of the RG flows, we demonstrate the collapse of the pseudogap for charge excitations (Mottness) at a quantum critical point (QCP) possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-pseudogapping near the antinodes. The QCP is characterised using both thermodynamic and quantum information-theoretic measures. d-wave superconducting order is shown to arise from this quantum critical state of matter. The pseudogap phase possesses a variety of fluctuations that lead to several symmetry-broken phases at low-energies. Benchmarking of the ground state energy per particle and the double-occupancy fraction obtained from a finite-size scaling analysis against existing numerical results yields excellent agreement. We present detailed insight into the T = 0 origin of several experimentally observed findings in the cuprates, including Homes law and Planckian dissipation. We also establish that the heirarchy of temperature scales for the pseudogap (T PG), onset temperature for pairing (T ons), formation of the Mott liquid (T ML) and superconductivity (T C) obtained from our analysis is quantitatively consistent with that observed experimentally for some members of the cuprates. Our results offer insight on the ubiquitous origin of superconductivity in doped Mott insulating states, and pave the way towards a systematic search for higher superconducting transition temperatures in such systems.
Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d(x(2)-y(2)) superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into seven distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only two, the transitions to d(x(2)-y(2))+is and d(x(2)-y(2))+id(xy) pairing, possess stable fixed points with universal damping of nodal quasiparticles; the latter leaves the gapped quasiparticles along (1,0), (0,1) essentially undamped.