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arXiv:cond-mat/0508251

Self-trapping phenomenon in (2+1)-dimensional quantum electrodynamics and its application to high-T_c cuprates with Neel ordering

Takao Morinari

Published Aug 10, 2005• 2 citations
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Abstract

The strong coupling effect in the (2+1)-dimensional quantum electrodynamics (QED_3) description of the $S=1/2$ Heisenberg antiferromagnet is studied in terms of a canonical transformation which has been used in the small polaron theory in electron-phonon systems. In the N{\' e}el ordered phase, we show that the Dirac fermions are localized and the spectral function is of the Gaussian form due to the coupling to the longitudinal gauge field. The width of the broad line shape is \sim 4J with J the superexchange interaction energy and the localization length is sim 3a, with a the lattice constant.

DOI
10.48550/arxiv.cond-mat/0508251

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Bulletin of Pure & Applied Sciences- Physics•Jan 1, 2022•0 citations
The strong coupling effect in the (2+1)-dimensional quantum electrodynamics (QED_3) description of the S=1/2S=1/2S=1/2 Heisenberg antiferromagnet is studied in terms of a canonical transformation which has been used in the small polaron theory in electron-phonon systems. In the N{' e}el ordered phase, we show that the Dirac fermions are localized and the spectral function is of the Gaussian form due to the coupling to the longitudinal gauge field. The width of the broad line shape is \sim 4J with J the superexchange interaction energy and the localization length is sim 3a, with a the lattice constant.
Theory of quantum electrodynamics in three spatial-time dimensions is applied to the two-dimensional S=1∕2S=1∕2S=1∕2 quantum Heisenberg antiferromagnet in order to investigate a doped hole in high-temperature superconductors. Strong coupling analysis of the U(1) gauge field interaction is carried out to describe spectral broadening observed in the undoped compounds. It is found that the fermionic quasiparticle spectrum is of Gaussian form with the width about 3J3J3J, with JJJ being the superexchange interaction energy. The energy shift of the spectrum is on the order of the quasiparticle bandwidth, which suggests that the system is in the strong coupling regime with respect to the gauge field interaction describing the phase fluctuations about the $\ensuremath{\pi}$-flux state.
Quantum electrodynamics in 2+1 dimensions ( QED3 ) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated J1−J2 Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from QED3 , in the quantum spin liquid regime. This evidence includes a large manifold of explicitly constructed monopole and bilinear excitations of QED3 , which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of emergent valence-bond solid (VBS) correlations, which can be interpreted either as evidence of critical VBS fluctuations of an emergent Dirac spin liquid or as a transition from the 120° Néel order to a VBS whose quantum critical point is described by QED3 . Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to N=48 sites. Published by the American Physical Society 2024
We present a detailed numerical study of the one-dimensional Holstein model with a view to understanding the self-trapping process of electrons or excitons in crystals with short-range particle-lattice interactions. Applying a very efficient variational Lanczos method, we are able to analyze the ground-state properties of the system in the weak- and strong-coupling, adiabatic and nonadiabatic regimes on lattices large enough to eliminate finite-size effects. In particular, we obtain the complete phase diagram and comment on the existence of a critical length for self-trapping in finite (closed) one-dimensional systems. In order to characterize large and small polaron states we calculate self-consistently the lattice distortions and the particle-phonon correlation functions. In the strong-coupling case, two distinct types of small polaron states are shown to be possible according to the relative importance of static displacement field and dynamic polaron effects. Special emphasis is on the intermediate-coupling regime, which we also study by means of direct diagonalization, preserving the full dynamics and quantum nature of phonons. The crossover from large to small polarons shows up in a strong decrease of the kinetic energy accompanied by a substantial change in the optical absorption spectra. We show that our numerical results in all important limiting cases reveal excellent agreement with both analytical perturbation theory predictions and very recent density matrix renormalization group data.
The antiferromagnetic phase of two-dimensional (2D) and three-dimensional (3D) Hubbard model with nearest neighbor hopping is studied on a bipartite cubic lattice by means of the quantum $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfy the Mermin-Wagner theorem. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin-quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. An effective action consisting of a spin-charge rotor and a fermionic field is derived as a function of the Coulomb repulsion UUU and hopping parameter ttt. At zero temperature, our theory describes the evolution from a Slater (U⪡t)(U⪡t)(U⪡t) to a Mott-Heisenberg (U⪢t)(U⪢t)(U⪢t) antiferromagnet. The results for zero-temperature sublatice magnetization (2D) and finite temperature (3D) phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U∕tU∕tU∕t are presented and the role of the spin Berry phase in the interaction driven crossover is analyzed.
Polaronic features of dopant-induced charge carriers are manifest in recent experiments on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4+y{\mathrm{CuO}}_{4+\mathit{y}}CuO4+y​ and ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Nix{\mathrm{Ni}}_{\mathit{x}}Nix​CuO4+y{\mathrm{CuO}}_{4+\mathit{y}}CuO4+y​. To study the formation of hole (bi)polarons in such systems exhibiting strong Coulomb interactions, the Holstein t-J model is examined by means of a variational diagonalization technqiue for a wide range of phonon frequencies and electron-phonon (EP) couplings on finite square lattices, up to 18 effective sites in size. Including static displacement field, polaron, and squeezing effects, our approach allows for the description of nearly free polarons in the weak-coupling limit as well as for adiabatic Holstein polarons and nonadiabatic Lang-Firsov polarons in the case of strong EP interactions. At low doping levels and low phonon frequencies we demonstrate that antiferromagnetic spin correlations and EP interactions reinforce each other to the effect of lowering the threshold for polaronic self-localization in a strongly distorted lattice. This is contrasted with the nonadiabatic regime, where we observe the formation of Lang-Firsov polarons with moderate polaronic mass enhancement in a nearly undistorted lattice. In the case of two doped holes, the hole binding energy is analyzed in detail and we find that hole binding is enhanced as a dynamical (static) effect of a rather weak (extremely strong) EP interaction for delocalized (self-trapped) polarons. At quarter-filling we notice, in the adiabatic regime, a sequence of transitions as the EP coupling increases from nearly free mobile polarons to a polaronic superlattice and finally to a charge-separated state. The ordering of polarons disappears at higher phonon frequencies.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.