We present quantum Monte Carlo results for a square-lattice S = 1/2 XY-model with a standard nearest-neighbor coupling J and a four-spin ring exchange term K. Increasing K/J, we find that the ground state spin-stiffness vanishes at a critical point at which a spin gap opens and a striped bondplaquette order emerges. At still higher K/J, this phase becomes unstable and the system develops a staggered magnetization. We discuss the quantum phase transitions between these phases.PACS numbers: 75.10.Jm, 75.40.Mg, Ring exchange interactions have for a long time been known to be present in a variety of quantum many-body systems [1] and have been investigated rather thoroughly in solid 3 He [2]. They are also important for electrons in the Wigner crystal phase [3,4]. In strongly correlated electron systems, such as the high-T c cuprates and related antiferromagnets, ring exchange processes are typically much weaker than the pair exchange J [5] and are often neglected. Four-spin ring exchange has, however, been argued to be responsible for distinct features in the magnetic Raman [6] and optical absorption spectra [7]. Neutron measurements of the magnon dispersion have also become sufficiently accurate to detect deviations from the standard pair exchange Hamiltonian (the Heisenberg model) and such discrepancies have been attributed to ring exchange [8,9]. Recently, ring exchange has attracted interest as a potentially important interaction that could lead to novel quantum states of matter, in particular 2D electronic spin liquids with fractionalized excitations [10,11,12,13,14,15]. Furthermore, for bosons on a square lattice ring exchange has been shown to give rise to a "exciton Bose liquid" phase [16].Here we study the effects of ring exchange in one of the most basic quantum many-body Hamiltonians-the spin-1/2 XY-model on a 2D square lattice. We use a quantum Monte Carlo method (stochastic series expansion, hereafter SSE [17,18,19]) to study the low-temperature behavior of this system including a four-spin ring term. Defining bond and plaquette exchange operatorsthe Hamiltonian iswhere ij denotes a pair of nearest-neighbor sites and ijkl are sites on the corners of a plaquette. For K = 0 this is the standard quantum XY-model, or, equivalently, hard-core bosons at half-filling with no interactions apart from the single-occupancy constraint. This system undergoes a Kosterlitz-Thouless transition at T /J ≈ 0.68 [20,21] and has a T = 0 ferromagnetic moment M x = S x i ≈ 0.44 [22,23]. The K-term corresponds to retaining only the purely x-and y-terms of the full cyclic exchange.In a soft-core version of the pure ring model (J = 0), Paramekanti et al. recently found a compressible but non-superfluid phase (exciton Bose liquid) for weak onsite repulsion U [16]. As the hard-core limit is approached they found a transition to a staggered chargedensity-wave phase. Hence, the ground state of the spin Hamiltonian (3) can be expected to change from an easyplane ferromagnet with a finite spin stiffness ρ s and a magnetization M x at...
We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.
We describe how density-matrix renormalization group (DMRG) can be used to solve the full-CI problem in quantum chemistry. As an illustration of the potential of this method, we apply it to a paramagnetic molecule. In particular, we show the effect of various basis set, the scaling as the fourth power of the size of the problem, and compare the DMRG with other methods. I. INTRODUCTIONFirst-principle quantum chemistry is employed successfully to obtain thermochemical data; molecular structures; force fields and frequencies; assignments of NMR-, photoelectron-, E.S.R-, and UV-spectra; transition state structures as well as activation barriers; dipole moments and other one-or two-electron properties. Two routes of calculation are available: (i) ab initio Hartree-Fock (HF) and post-HF methods; and (ii) density functional theory (DFT). Though both approaches are rigorous, the former one necessitates lengthy configuration interaction (CI) treatment to account for electron correlation; whereas the latter one crucially depends upon the quest for accurate exchange and correlation functionals. The recently acquired popularity of DFT stems in large measure from its computational efficiency, allowing it to treat medium to large size molecules at a fraction of the time required for HF or post-HF calculations. More importantly, expectation values derived from DFT are, in most cases, better in line with experiment than results obtained from HF calculations. This is particularly the case for systems involving transition metals. Nevertheless, if one wants to achieve experimental accuracy for small polyatomic molecules, the method reaches its limits. On the other hand, post-HF overcomes these limits and goes even beyond experimental accuracy, e.g. in case of H 2 . The drawback is of course its very high cost in computational power. However these very accurate calculations of small systems may provide the best route to obtaining more accurate exchange-correlation potentials using the constrained search algorithm of Levy [1].Keeping the discussion to ab initio (HF and post-HF) quantum chemistry, let us now consider the state of the art in this topic. We now know how to do very large calculations, using the direct methodology [2]. We can also manage to work with good basis sets for such calculations, although it is considered that 6-31G* are not good enough, and probably something nearer to TZ2P is required for definitive SCF calculations. Beyond SCF there are major difficulties, all associated with trying to more accurately represent the electron-electron cusp. We know from the work of Kutzelnigg [3], that the convergence of this problem is very slow, something like (ℓ + 1 2 ) −4 , with ℓ the orbital angular momentum quantum number. This means that very large basis sets are required for correlated calculations. We know that it is more important to include d and f basis functions than to improve the methodology (e.g. 6-31G* basis are not appropriate for correlated studies). We also know that the raw cost of the main correlated method...
We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the Density-Matrix Renormalization Group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the onedimensional Heisenberg phase. At large on-site Coulomb repulsion U , we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak U , sufficiently large next-nearest-neighbor hopping t2 leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As U is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.The one-dimensional Hubbard model is the prototypical model for strongly interacting electrons in one dimension. For repulsive interaction, its low-energy, longdistance physics is well-described by the Luttinger liquid picture, in which the fundamental excitations are gapless bosonic spin and charge modes, and the correlation functions exhibit critical behavior with non-universal exponents 1 . At half filling, Umklapp processes lead to a gap in the charge excitation spectrum and thus insulating behavior for any finite value of the on-site Coulomb interaction, U . The spin excitations behave as in the strong-coupling, Heisenberg limit, i.e. are gapless with linear dispersion.The introduction of a next-nearest-neighbor hopping can change this picture dramatically. In strong coupling, the additional hopping leads to a frustrating next-nearest-neighbor Heisenberg interaction so that the model maps to the frustrated Heisenberg chain. At weakcoupling, the effect of t 2 is to change the band structure, and, in particular, the number of Fermi points. In this paper, we shall explore the interplay between the frustration at strong coupling and the changed band structure at weak coupling. As we shall see, the resulting phase diagram contains a number of highly interesting phases: a spin-gapped metallic phase, commensurate and incommensurate disordered magnetic insulating phases, as well as the one-dimensional Heisenberg insulator.We study the Hamiltonianwhere t 1 is the nearest-neighbor and t 2 the next-nearest neighbor hopping and U is the on-site Coulomb repulsion. It is useful to visualize the geometry as a zigzag structure as depicted in Fig. 1. Here the summation goes over L sites and spin σ, and we will always take U positive and set t 1 = 1. Since the sign of t 2 is irrelevant at half filling due to particlehole symmetry, we only consider t 2 > 0 in the following. For U = 0 and periodic boundary conditions, H can be diagonalized via a Fourier transform, yieldingwith k an integer multiple of 2π L andAn interesting feature of this band structure is that there is a nontrivial transition as a function of t 2 even at U = 0. For t 2 < 0.5, the noninteracting ...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.