Showing papers by "Subir Sachdev published in 1999"

Quantum phase transitions

Abstract: Nature abounds with phase transitions. The boiling and freezing of water are everyday examples of phase transitions, as are more exotic processes such as superconductivity and superfluidity. The universe itself is thought to have passed through several phase transitions as the high-temperature plasma formed by the big bang cooled to form the world as we know it today.

Charge Order, Superconductivity, and a Global Phase Diagram of Doped Antiferromagnets

Abstract: We investigate the interplay between lattice symmetry breaking and superconducting order in a two-dimensional model of doped antiferromagnets, with long-range Coulomb interactions and $\mathrm{Sp}(2N)$ spin symmetry, in the large- $N$ limit. Our results motivate the outline of a global phase diagram for the cuprate superconductors. We describe the quantum transitions between the phases, the evolution of their fermion excitation spectrum, and the experimental implications.

Quantum Impurity in a Nearly Critical Two Dimensional Antiferromagnet

Abstract: The spin dynamics of an arbitrary localized impurity in an insulating two-dimensional antiferromagnet, across the host transition from a paramagnet with a spin gap to a Neel state, is described. The impurity spin susceptibility has a Curie-like divergence at the quantum-critical coupling, but with a universal effective spin that is neither an integer nor a half-odd integer. In the Neel state, the transverse impurity susceptibility is a universal number divided by the host spin stiffness (which determines the energy cost to slow twists in the orientation of the Neel order). These and numerous other results for the thermodynamics, Knight shift, and magnon damping have important applications in experiments on layered transition metal oxides.

Universal relaxational dynamics near two-dimensional quantum critical points

Abstract: We describe the nonzero temperature $(T)$, low frequency $(\ensuremath{\omega})$ dynamics of the order parameter near quantum critical points in two spatial dimensions $(d)$, with a special focus on the regime $\ensuremath{\Elzxh}\ensuremath{\omega}\ensuremath{\ll}{k}_{B}T$. For the case of a ``relativistic,'' $\mathrm{O}(n)$-symmetric, bosonic quantum field theory we show that, for small $\ensuremath{\epsilon}=3\ensuremath{-}d$, the dynamics is described by an effective classical model of waves with a quartic interaction. We provide analytical and numerical analyses of the classical wave model directly in $d=2$. We describe the crossover from the finite frequency, ``amplitude fluctuation,'' gapped quasiparticle mode in the quantum paramagnet (or Mott insulator), to the zero frequency ``phase'' $(ng~2)$ or ``domain wall'' $(n=1)$ relaxation mode near the ordered state. For static properties, we show how a surprising, duality-like transformation allows an exact treatment of the strong-coupling limit for all n. For $n=2$, we compute the universal T dependence of the superfluid density below the Kosterlitz-Thouless temperature, and discuss implications for the high temperature superconductors. For $n=3$, our computations of the dynamic structure factor relate to neutron scattering experiments on ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{Cu}\mathrm{}\mathrm{O}}_{4}$, and to light scattering experiments on double layer quantum Hall systems. We expect that closely related effective classical wave models will apply also to other quantum critical points in $d=2$. Although computations in appendixes do rely upon technical results on the $\ensuremath{\epsilon}$-expansion of quantum critical points obtained in earlier papers, the physical discussion in the body of the paper is self-contained, and can be read without consulting these earlier works.

Translational symmetry breaking in two-dimensional antiferromagnets and superconductors

Abstract: It was argued many years ago that translational symmetry breaking due to the appearance of spin-Peierls ordering (or bond-charge stripe order) is a fundamental property of the quantum paramagnetic states of a large class of square lattice antiferromagnets. Recently, such states were shown to be a convenient point of departure for studying translational symmetry breaking in doped antiferromagnets: these results are briefly reviewed here with an emphasis on experimental implications. In the presence of stronger frustration, it was also argued that the insulating antiferromagnet can undergo a transition to a deconfined state with no lattice symmetry breaking. This transition is described by a fully-frustrated Ising model in a transverse field: details of this earlier derivation of the Ising model are provided here--this is motivated by the reappearance of the same Ising model in a recent study of the competition between antiferromagnetism and d-wave superconductivity by Senthil and Fisher (cond-mat/9910224).

Intermediate-temperature dynamics of one-dimensional heisenberg antiferromagnets

Abstract: We present a general theory for the intermediate temperature (T ) properties of Heisenberg antiferromagnets of spin-S ions on p-leg ladders, valid for 2Sp even or odd. Following an earlier proposal for 2Sp even (Damle and Sachdev, Phys. Rev. B57, 8307), we argue that an integrable, classical, continuum model of a xed-length, 3-vector applies over an intermediate temperature range; this range becomes very wide for moderate and large values of 2Sp. The coupling constants of the eective model are known exactly in terms of the energy gap above the ground state (for 2Speven), or a crossover scaleT0 (for 2Sp odd). Analytic and numeric results for dynamic and transport properties are obtained, including some exact results for the spin-wave damping. Numerous quantitative predictions for neutron scattering and NMR experiments are made. A general discussion on the nature of T> 0 transport in integrable systems is also presented: an exact solution of a toy model proves that diusion can exist in integrable systems, provided proper care is taken in approaching the thermodynamic limit.

Quantum conductors in a plane

Abstract: When electrons are confined to move in a plane, strange things happen. For example, under normal circumstances, they are not expected to conduct electricity at low temperatures. The absence of electrical conduction in two dimensions (2D) at zero temperature has been one of the most cherished paradigms in solid-state physics (1). In fact, the 1977 physics Nobel Prize was awarded, in part, for the formulation of the basic principle on which this result is based. However, recent experiments (2) on a dilute electron gas confined to move at the interface between two semiconductors pose a distinct counterexample to the standard view. Transport measurements reveal (2) that as the temperature is lowered, the resistivity drops without any signature of the anticipated up-turn as required by the standard account. It is the possible existence of a new conducting state and hence a new quantum phase transition in 2D that is the primary focus of this session. In the absence of a magnetic field, the only quantum phase transition known to exist in 2D that involves a conducting phase is the insulator–superconductor transition (for a review, see ref. 3). Consequently, this session focuses on the general properties of quantum phase transitions, the evidence for the new conducting state in a 2D electron gas, and the range of phenomena that can occur in insulator–superconductor transitions. Unlike classical phase transitions, such as the melting of ice, all quantum phase transitions occur at the absolute zero of temperature. Although initially surprising, this state of affairs is expected, as quantum mechanics is explicitly a zero-temperature theory of matter. As such, quantum phase transitions are not controlled by changing system parameters such as the temperature as in the melting of ice, but rather by changing some external parameter such as the number of defects or the magnitude of …

Quantum phase transitions in antiferromagnets and superfluids

Abstract: We present a general introduction to the non-zero temperature dynamic and transport properties of low-dimensional systems near a quantum phase transition. Basic results are reviewed in the context of experiments on the spin-ladder compounds, insulating two-dimensional antiferromagnets, and double-layer quantum Hall systems. Recent large N computations on an extended t-J model (cond-mat/9906104) motivate a global scenario of the quantum phases and transitions in the high temperature superconductors, and connections are made to numerous experiments.