Phase String Research Articles

Lower pseudogap phase of Mott insulators: A spin/vortex liquid state

The pseudogap phase is considered to be a new state of matter in the phase string model of the doped Mott insulator, which is composed of two distinct regimes known as the upper and lower pseudogap phases, respectively. The former corresponds to the formation of spin-singlet pairing, the magnetic characterizations of which have been recently studied [Phys. Rev. B 72, 104520 (2005)]. The latter, as a low-temperature regime of the pseudogap phase, is systematically explored in this work, which is characterized by the formation of the Cooper pair amplitude and described by a generalized Ginzburg-Landau theory. Elementary excitation in this phase is a charge-neutral object carrying spin-$1∕2$ and locking with a supercurrent vortex, known as a spinon-vortex composite. Such a lower pseudogap phase can be regarded as a vortex liquid state due to the presence of free spinon vortices. Here thermally excited spinon vortices destroy the phase coherence and are responsible for the nontrivial Nernst effect and diamagnetism. The transport entropy and core energy associated with a spinon vortex are determined by the spin degrees of freedom. Such a spontaneous vortex liquid phase can be also considered as a spin liquid with a finite correlation length and gaped $S=1∕2$ excitations, where a resonancelike nonpropagating spin mode emerges at the antiferromagnetic wavevector $(\ensuremath{\pi},\ensuremath{\pi})$ with a doping-dependent characteristic energy. The superconducting phase is closely related to the lower pseudogap phase by a topological transition with spinon vortices and antivortices forming bound pairs and the emergence of fermionic quasiparticles as holon-spinon-vortex bound objects. A quantitative phase diagram in the parameter space of doping, temperature, and magnetic field is determined. Comparisons with experiments are also made.

Spin Hall effect in a doped Mott insulator

The existence of conserved spin Hall currents is shown in a strongly correlated system without involving spin-orbit coupling. The spin Hall conductivity is determined by intrinsic bulk properties, which remains finite even when the charge resistivity diverges in strong magnetic fields at zero temperature. The state in the latter limit corresponds to a spin Hall insulator. Such a system is a doped Mott insulator described by the phase string theory, and the spin Hall effect is predicted to coexist with the Nernst effect to characterize the intrinsic properties of the low-temperature pseudogap phase.

Microscopic origin of local moments in a zinc-doped high-Tcsuperconductor

The formation of a local moment around a zinc impurity in the high-$T_{c}$ cuprate superconductors is studied within the framework of the bosonic resonating-valence-bond (RVB) description of the $t-J$ model. A topological origin of the local moment has been shown based on the phase string effect in the bosonic RVB theory. It is found that such an $S=1/2$ moment distributes near the zinc in a form of staggered magnetic moments at the copper sites. The corresponding magnetic properties, including NMR spin relaxation rate, uniform spin susceptibility, and dynamic spin susceptibility, etc., calculated based on the theory, are consistent with the experimental measurements. Our work suggests that the zinc substitution in the cuprates provide an important experimental evidence for the RVB nature of local physics in the original (zinc free) state.

Spin dynamics in a doped-Mott-insulator superconductor

We present a systematic study of spin dynamics in a superconducting ground state, which itself is a doped-Mott-insulator and can correctly reduce to an antiferromagnetic (AF) state at half-filling with an AF long-range order (AFLRO). Such a doped Mott insulator is described by a mean-field theory based on the phase string formulation of the t-J model. We show that the spin wave excitation in the AFLRO state at half-filling evolves into a resonancelike peak at a finite energy in the superconducting state, which is located around the AF wave vectors. The width of such a resonancelike peak in momentum space decides a spin correlation length scale which is inversely proportional to the square root of doping concentration, while the energy of the resonancelike peak scales linearly with the doping concentration at low doping. An important prediction of the theory is that, while the total spin sum rule is satisfied at different doping concentrations, the weight of the resonancelike peak does not vanish, but is continuously saturated to the weight of the AFLRO at zero-doping limit. Besides the low-energy resonancelike peak, we also show that the high-energy excitations still track the spin wave dispersion in momentum space, contributing to a significant portion of the total spin sum rule. The fluctuational effect beyond the mean-field theory is also examined, which is related to the broadening of the resonancelike peak in energy space. In particular, we discuss the incommensurability of the spin dynamics by pointing out that its visibility is strongly tied to the low-energy fluctuations below the resonancelike peak. We finally investigate the interlayer coupling effect on the spin dynamics as a function of doping, by considering a bilayer system.

Topological gauge structure and phase diagram for weakly doped antiferromagnets.

We show that a topological gauge structure in an effective description of the t-J model gives rise to a global phase diagram of antiferromagnetic and superconducting phases in a weakly doped regime. Dual confinement and deconfinement of holons and spinons play essential roles here, with a quantum critical point at a doping concentration x(c) approximately equal to 0.043. The complex experimental phase diagram at low doping is well described within such a framework.

Quasiparticles as composite objects in the resonating valence bond superconductor

We study the nature of the superconducting state, the origin of d-wave pairing, and elementary excitations of a resonating valence bond (RVB) superconductor. We show that the phase string formulation of the t-J model leads to confinement of bare spinon and holon excitations in the superconducting state, though the vacuum is described by the RVB state. Nodal quasiparticles are obtained as composite excitations of spinon and holon excitations. The d-wave pairing symmetry is shown to arise from short range antiferromagnetic correlations.

Spontaneous vortex phase in the bosonic resonating valence bond theory

In the description of spin-charge separation based on the phase string theory of the $t\ensuremath{-}J$ model, spinon excitations are vortices in the superconducting state. Thermally excited spinons destroy phase coherence, leading to a new phase characterized by the presence of free spinon vortices at temperatures ${T}_{c}<T<{T}_{v}.$ The temperature scale ${T}_{v}$ at which holon condensation occurs marks the onset of the pairing amplitude and is related to the spin-pseudogap temperature ${T}^{*}.$ The phase below ${T}_{v},$ called the spontaneous vortex phase, shows novel transport properties before phase coherence sets in at ${T}_{c}.$ We discuss the Nernst effect as an intrinsic characterization of such a phase, in comparison with recent experimental measurements.

Random Matrix Approach to a Special Kind of Quantum Random Hopping

We use the random matrix method to study one kind of quantum random hopping. TheHamiltonian is a non-Hermitian matrix with some negative subdiagonalelements. Using potential theory, we calculate the eigenvalue density ofan N×N matrix when N goes to infinity. We also obtain a least upper boundof the module of eigenvalues. In view of phase string theory in high-temperaturesuperconductors, this model connects withlocalization-delocalization transition.

Lattice study of3Dcompact QED at finite temperature

We study the deconfinement phase transition and monopole properties in a finite temperature three-dimensional compact Abelian gauge model on the lattice. We predict the critical coupling as a function of the lattice size in a simplified model to describe monopole binding. We demonstrate numerically that monopoles are sensitive to the transition. In the deconfinement phase the monopoles appear in the form of a dilute gas of magnetic dipoles. In the confinement phase both monopole density and string tension differ from semiclassical estimates if monopole binding is neglected. However, an analysis of the monopole clusters shows that the relation between the string tension and the density of monopoles in charged clusters is in reasonable agreement with predictions. We study the cluster structure of the vacuum in both phases of the model.

Spin-charge separation in the single-hole-doped Mott antiferromagnet

The motion of a single hole in a Mott antiferromagnet is investigated based on the t-J model. An exact expression of the energy spectrum is obtained, in which the irreparable phase string effect [Phys. Rev. Lett. 77, 5102 (1996)] is explicitly present. By identifying the phase string effect with spin backflow, we point out that spin-charge separation must exist in such a system: the doped hole has to decay into a neutral spinon and a spinless holon, together with the phase string. We show that while the spinon remains coherent, the holon motion is deterred by the phase string, resulting in its localization in space. We calculate the electron spectral function which explains the line shape of the spectral function as well as the ``quasiparticle'' spectrum observed in angle-resolved photoemission experiments. Other analytic and numerical approaches are discussed based on the present framework.

Understanding high-T c cuprates based on the phase string theory of doped antiferromagnet

We present a self-consistent RVB theory which unifies the metallic (superconducting) phase with the half-filling antiferromagnetic (AF) phase. Two crucial factors in this theory include the RVB condensation which controls short-range AF spin correlations and the phase string effect introduced by hole hopping as a key doping effect. We discuss both the uniform and non-uniform mean-field solutions and show the unique features of the characteristic spin energy scale, superconducting transition temperature, and the phase diagram, which are all consistent with the experimental measurements of high-T c cuprates.

Two-legt−Jladder: A mean-field description

Two-leg t-J ladders are investigated in the framework of a combination of the phase string formulation and bond-operator representation. We develope a mean-field theory in the strong rung interaction regime, i.e. $J_{\perp}\gg J, t$, which provides a unified description of the undoped insulating phase and the low doping phase --- the so-called C1S0 phase. Both of them are characterized by the resonating-valence-bond (RVB) order parameter, with gap opened up in all spin excitations. The ground state of the doped phase is intrinsically a superconductor with a d-wave symmetry, which is driven by the RVB correlations. The ground-state energy is in good agreement with numerical results. Phase separation is shown to occur beyond some critical value of J/t for given doping concentration. We also show that the spin gap in the doped phase is determined by quasi-particle-like excitations. The local structure of hole pairs as well as the spectra of various spin and charge modes are analyzed in comparison with other approaches.

Mean-field description of the phase string effect in thet−Jmodel

A mean-field treatment of the phase string effect in the $t\ensuremath{-}J$ model is presented. Such a theory is able to unite the antiferromagnetic (AF) phase at half-filling and the metallic phase at finite doping within a single theoretical framework. We find that the low-temperature occurrence of the AF long-range ordering (AFLRO) at half-filling and superconducting condensation in the metallic phase are all due to Bose condensations of spinons and holons, respectively, on the top of a spin background described by bosonic resonating-valence-bond pairing. The fact that both spinon and holon here are bosonic objects, as the result of the phase string effect, represents a crucial difference from the conventional slave-boson and slave-fermion approaches. This theory also allows an underdoped metallic regime where the Bose condensation of spinons can still exist. Even though the AFLRO is gone here, such a regime corresponds to a microscopic charge inhomogeneity with short-ranged spin ordering. We discuss some characteristic experimental consequences for those different metallic regimes. A perspective on broader issues based on the phase string theory is also discussed.

UNDERDOPING VERSUS OPTIMUM-DOPING: A BOSONIC RVB UNDERSTANDING

We propose that the bosonic RVB description of spins and the phase string effect of doping constitute two crucial factors in the weakly-doped t– J model. Within this framework, a charge inhomogeneity solution is found in the underdoped metallic phase, characterized by a double-peak energy structure in dynamic spin susceptibility in contrast to a single `resonance-like' peak below T c at `optimum'-doping. Comparisons with recent experimental measurements on cuprates are made.

Bosonic Resonating-Valence-Bond Description of a Doped Antiferromagnet

We propose a theory for a doped antiferromagnet based on the bosonic resonating-valence-bond (RVB) description incorporating the phase string effect. Both antiferromagnetic and superconducting phase transitions occur naturally inside such a bosonic RVB phase. Two distinct metallic regions---underdoping and optimum doping---are also found to be a logical consequence; their unique features explain the recent neutron-scattering measurements in cuprates.

Spin-charge separation in angle-resolved photoemission spectra

The implications of angle-resolved photoemission spectroscopy on the issue of spin-charge separation are discussed from the viewpoint of slave-particle resonating-valence-bond theories. It is pointed out that the nonlocal phase string is essential to reproduce the two-peak structure experimentally observed in SrCuO${}_{2}$. The comparison between one-dimensional and two-dimensional cases is also made.

Phase string effect in the t-J model: General theory

We reexamine the problem of a hole moving in an antiferromagnetic spin background and find that the injected hole will always pick up a sequence of nontrivial phases from the spin degrees of freedom. Previously unnoticed, such a stringlike phase originates from the hidden Marshall signs which are scrambled by the hopping of the hole. We can rigorously show that this phase string is nonrepairable at low energy and give a general proof that the spectral weight Z must vanish at the ground-state energy due to the phase-string effect. Thus, the quasiparticle description fails here and the quantum interference effect of the phase string dramatically affects the long-distance behavior of the injected hole. We introduce a so-called phase-string formulation of the t-J model for a general number of holes in which the phase-string effect can be explicitly tracked. As an example, by applying this new mathematical formulation in one dimension, we reproduce the well-known Luttinger-liquid behaviors of the asymptotic single-electron Green's function and the spin-spin correlation function. We can also use the present phase-string theory to justify previously developed spin-charge separation theory in two dimensions, which offers a systematic explanation for the transport and magnetic anomalies in the high-${\mathrm{T}}_{\mathrm{c}}$ cuprates.

Phase String Effect in a Doped Antiferromagnet.

Based on the $t\ensuremath{-}J$ model, it is shown that a hole moving on an antiferromagnetic spin background always induces a phase-string effect. Such a previously unnoticed phase string is revealed by explicitly tracking the Marshall sign and can be rigorously shown to be nonrepairable at low energy. Its quantum interference can drastically modify the long-wavelength behavior of the doped hole, leading to a vanishing spectral weight $Z$ at the ground-state energy. Implication for finite doping is also discussed.

Phase Transition and String Formation in Six-Dimensional Gauge Theory

We consider an SU(2) gauge theory in six-dimensions. We show that there exists non-trivial structure of gauge vacua in compactified background M4xS2. In this circumstances, there can exist a cosmic string, whose solution is recently constructed by the present authors. We consider the stage of the formation of the strings, i.e., the phase transition of the gauge configuration on the sphere in the `hot' early universe. We find that if SU(2)-doublet fermions are the dominant component of the radiation at high temperatures, the phase transition successively occurs after the spontaneous-compactification transition. Otherwise, non-trivial vacuum with `monopole' configuration of the SU(2) gauge field never appears globally and strings must be formed at the same time as the extra space is compactified.

Phase Transition and String Formation in Six-Dimensional Gauge Theory

Phase Transition and String Formation in Six-Dimensional Gauge Theory