Smooth boundary conditions for quantum lattice systems

Vekić, M.; White, Steven R.

doi:10.1103/physrevlett.71.4283

Cited by 66 publications

(70 citation statements)

References 8 publications

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“…3(b), using DMRG on 200 rungs with smooth boundary conditions. 81 By performing a finite-size scaling using systems with up to 400 rungs, we estimate the finite-size effects to be comparable to the size of the symbols in Fig. 3(b).…”

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confidence: 98%

Topological phases in ultracold polar-molecule quantum magnets

et al. 2013

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We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases-previously studied only in the nearestneighbor case-survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed. have spurred tremendous interest in exotic strongly correlated many-body phenomena arising from anisotropic, long-ranged dipole-dipole interactions. The types of anisotropies realizable with these interactions are typically limited to simple changes of the interaction sign and magnitude according to the spherical harmonic Y 2,0 ∝ 1 − 3 cos 2 θ , where (θ,φ) are the spherical coordinates of the vector connecting the two interacting dipoles. 11,13,32,33 In this Rapid Communication we show, in the context of polar molecules, that microwave dressing provides a tremendous degree of simultaneous control over five independent dipoledipole interaction terms whose angular dependences are given by the rank-2 spherical harmonics. This opens the door to simulating well-known models including the spin-1/2 XXZ model with a direction-dependent spin anisotropy, the spin-1 bilinear-biquadratic model, 47 and the Kitaev honeycomb model. 48 Thanks to the use of direct dipole-dipole coupling, the resulting interactions are stronger and hence easier to observe experimentally than other-potentially direction-dependentspin-spin interactions such as superexchange in ultracold atoms 49 or perturbative dipole-dipole-mediated couplings between polar molecules. 16,17 As a specific example demonstrating the reach of our method, we show how to design a spin-1/2 XXZ model with direction-dependent spin anisotropy using a minimal and experimentally reasonable microwave configuration. In a two-legged ladder geometry with nearest-neighbor interactions, this model has been shown to exhibit symmetry protected topological (SPT) phases. 50 These phases are exotic gapped states of matter distinct from trivial gapped phases when specific symmetries are present. A lattice of polar molecules in the XY plane is subjected to a dc electric field alongẑ. We define the xyz coordinate system as the rotation of the XYZ coordinate system around Z by 0 and then aroundŷ by 0 . A vector R with polar coordinates (R, ) in the XY plane has spherical coordinates (R,θ,φ) in the xyz coordinate system. method (DMRG), 64 we compute the phase diagram of the two-legged-ladder model obtai...

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confidence: 98%

Topological phases in ultracold polar-molecule quantum magnets

et al. 2013

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“…We can improve effeciency of the calculation in the parameter range by using a different boundary condition other than the usual open boundary condition (OBC). 17,22,23) The idea is to make the energy scale near the boundary of the lead small by reducing the hopping amplitude exponentially towards the edges of the system, thus including the lower energy excitations. There are of course several possible ways of reducing the hopping parameters.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…There are of course several possible ways of reducing the hopping parameters. In this paper we use the smooth boundary condition 22) (SBC) by setting the 10 hopping parameters from the edge as…”

Section: Boundary Conditionsmentioning

confidence: 99%

Time-Dependent DMRG Study on Quantum Dot under a Finite Bias Voltage

et al. 2008

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Resonant tunneling through quantum dot under a finite bias voltage at zero temperature is investigated by using the adaptive time-dependent density matrix renormalization group (TdDMRG) method. Quantum dot is modeled by the Anderson Hamiltonian with the one-dimensional nearest-neighbor tightbinding leads. Initially the ground state wave function is calculated with the usual DMRG method. Then the time evolution of the wave function due to the slowly changing bias voltage between the two leads is calculated by using the TdDMRG technique. Even though the system size is finite, the expectation values of current operator show steady-like behavior for a finite time interval, in which the system is expected to resemble the real nonequilibrium steady state of the infinitely long system. We show that from the time intervals one can obtain quantitatively correct results for differential conductance in a wide range of bias voltage. Finally we observe an anomalous behavior in the expectation value of the double occupation operator at the dot hn " n # i as a function of bias voltage.

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“…There is a way to reduce the effect of boundaries in the DMRG scheme by turning off the interactions smoothly around the edges, which is called smooth boundary conditions [1,2]. Similar but modified boundary conditions apply to calculations of transport properties such as the conductance of one-dimensional (1D) interacting systems [3].…”

Section: Introductionmentioning

confidence: 99%

Sine-square deformation of solvable spin chains and conformal field theories

Katsura¹

2012

J. Phys. A: Math. Theor.

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Abstract. We study solvable spin chains, one-dimensional massless Dirac fermions, and conformal field theories (CFTs) with sine-square deformation (SSD), in which the Hamiltonian density is modulated by the function f (x) = sin 2 (πx/ℓ), where x is the position and ℓ is the length of the system. For the XY chain and the transverse field Ising chain at criticality, it is shown that the ground state of an open system with SSD is identical to that of a uniform chain with periodic boundary conditions. The same holds for the massless Dirac fermions with SSD, corresponding to the continuum limit of the gapless XY chain. For general CFTs, we find that the Hamiltonian of a system with SSD has an expression in terms of the generators of the Virasoro algebra. This allows us to show that the vacuum state is an exact eigenstate of the sine-square deformed Hamiltonian. Furthermore, for a restricted class of CFTs associated with affine Lie (Kac-Moody) algebras, including c = 1 Gaussian CFT, we prove that the vacuum is an exact ground state of the deformed Hamiltonian. This explains why the SSD has succeeded in suppressing boundary effects in one-dimensional critical systems, as observed in previous numerical studies.

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Smooth boundary conditions for quantum lattice systems

Cited by 66 publications

References 8 publications

Topological phases in ultracold polar-molecule quantum magnets

Topological phases in ultracold polar-molecule quantum magnets

Time-Dependent DMRG Study on Quantum Dot under a Finite Bias Voltage

Sine-square deformation of solvable spin chains and conformal field theories

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