Lattice Laughlin states of bosons and fermions at filling fractions 1/<i>q</i>

Tu, Hong-Hao; Nielsen, Anne E. B.; Cirac, J. I.; Sierra, Germȧn

doi:10.1088/1367-2630/16/3/033025

Cited by 61 publications

(128 citation statements)

References 40 publications

Supporting

Mentioning

122

Contrasting

Order By: Relevance

“…For the q ( 2, ) 1 2 η = state we find a good agreement of this formula for K 0.494 = , A 0.123 = . This suggest that this state in one dimension is well described by a Tomonaga-Luttinger liquid with central charge c = 1 and Luttinger parameter K 0.5 = , which corresponds to the properties of a free-boson CFT with radius 2 , as was the case for the corresponding one-dimensional Laughlin state [30].…”

Section: One Dimensional Critical Statesmentioning

confidence: 65%

“…In this section we consider a two dimensional lattice defined on a disk  of radius R → ∞ and show that the CFT states we have introduced reduce to Moore-Read states of particles in the continuum, that is (1), when N 0, η → →∞and the number of particles M is fixed. We restrict ourselves to lattices where the area per site a i is constant equal to a, but the derivation remains true for any lattice if we make η position dependent [30].…”

Section: The Cft States Become Moore-read States In the Continuum Limitmentioning

confidence: 99%

“…To compute the topological entanglement entropy of the state, the cylinder is cut into two halves and the Renyi entropy of the first half is computed using a Metropolis-Hastings algorithm. The topological entanglement entropy is then extracted by varying the size L y of the cylinder(30).…”

mentioning

confidence: 99%

See 2 more Smart Citations

Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

et al. 2015

Self Cite

View full text Add to dashboard Cite

We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1 2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction q 1 , which are non-Abelian fractional quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore-Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for some of the states we introduce in 2D, which suggests that the topological properties of the lattice states are the same as in the continuum, while the 1D states are critical states. We then derive exact parent Hamiltonians for these states on lattices of arbitrary size. By deforming these parent Hamiltonians, we construct local Hamiltonians that stabilize some of the states we introduce in 1D and in 2D.

show abstract

Section: One Dimensional Critical Statesmentioning

confidence: 65%

Section: The Cft States Become Moore-read States In the Continuum Limitmentioning

confidence: 99%

See 1 more Smart Citation

Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…As discussed in [5,31,42], (8) is a slightly modified version of the Kalmeyer-Laughlin state [43,44], which, up to some phase factors, is the ν = 1/2 Laughlin state with the possible particle positions limited to the sites of a square (or triangular) lattice. In fact, (8) reduces exactly to the Kalmeyer-Laughlin state in the thermodynamic limit [5,42]. Several topological properties of (8) have been analyzed in [31] and are in agreement with those of the ν = 1/2 Laughlin state in the continuum.…”

Section: A Fermi-hubbard-like Modelmentioning

confidence: 99%

“…If this symmetry is not present in a given setup, the field E bz should be replaced by two fields with different frequencies and appropriate polarizations. Note also that the optical lattice automatically shifts away the energies of the states |0,3/2,3/2 F and |0,3/2,−3/2 F [see (42) and (45) and Fig. 10] such that these states can be ignored in the following.…”

Section: Light Fieldsmentioning

confidence: 99%

Optical-lattice implementation scheme of a bosonic topological model with fermionic atoms

2014

Self Cite

View full text Add to dashboard Cite

We present a scheme to implement a Fermi-Hubbard-like model in ultracold atoms in optical lattices and analyze the topological features of its ground state. In particular, we show that the ground state for appropriate parameters has a large overlap with a lattice version of the bosonic Laughlin state at filling factor one-half. The scheme utilizes laser assisted and normal tunneling in a checkerboard optical lattice. The requirements on temperature, interactions, and hopping strengths are similar to those needed to observe the Néel antiferromagnetic ordering in the standard Fermi-Hubbard model in the Mott insulating regime.

show abstract

Infinite Dimensional Matrix Product States for Long-Range Quantum Spin Models

Bondesan

Quella

2016

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

We construct 1D and 2D long-range SU(N ) spin models as parent Hamiltonians associated with infinite matrix product states. The latter are constructed from correlators of primary fields in the SU(N ) 1 WZW model. Since the resulting groundstates are of Gutzwiller-Jastrow type, our models can be regarded as lattice discretizations of fractional quantum Hall systems. We then focus on two specific types of 1D spin chains with spins located on the unit circle, a uniform and an alternating arrangement. For an equidistant distribution of identical spins we establish an explicit connection to the SU(N ) Haldane-Shastry model, thereby proving that the model is critical and described by a SU(N ) 1 WZW model. In contrast, while turning out to be critical as well, the alternating model can only be treated numerically. Our numerical results rely on a reformulation of the original problem in terms of loop models. IntroductionLong-range spin models such as the Gaudin model [1] or the Haldane-Shastry model [2,3] have attracted the attention of physicists and mathematicians for a long period of time. In its original formulation, the Haldane-Shastry model describes the dynamics of SU(2) spins on a circle with inverse distance square interactions. It received a lot of attention due to its exact solvability and due to the form of its groundstate which is closely related to a bosonic Laughlin wavefunction at filling fraction ν = 1/2. The Haldane-Shastry model can be viewed as realizing a 1D analogue of a chiral spin liquid, with spinon excitations satisfying a generalized Pauli exclusion principle and obeying fractional statistics [4]. Many of the remarkable properties of the Haldane-Shastry model have their origin in the existence of an infinite-dimensional Yangian symmetry [5]. The latter also allowed to identify its thermodynamic limit as the SU(2) WZW conformal field theory at level k = 1 [6] (see also [7]). The Haldane-Shastry model admits obvious generalizations to symmetry groups such as the unitary series SU(N ) [5] or its supersymmetric analog SU(M |N ) [8,9].For our current work, there are two aspects of the SU(N ) Haldane-Shastry model that will be particularly important. First of all, it provides an efficient discretization of the SU(N ) WZW conformal field theory at level k = 1, where the scaling laws are not affected by logarithmic corrections. Secondly, wavefunctions of the groundstate as well as the excited states exhibit an intimate relation to the physics of fractional quantum Hall (FQH) systems, also for general values of N [10]. There are of course also differences: While the constituents of FQH systems are particles which are moving on a 2D surface, the degrees of freedom in the spin model are pinned to fixed discrete locations on a circle.The study of fractional quantum Hall systems is frequently based on the following intriguing dichotomy: One single chiral 2D conformal field theory (CFT) describes the two complementary aspects of the physical sample -its bulk and its boundary. It is known since the work of Mo...

show abstract

Lattice Laughlin states of bosons and fermions at filling fractions 1/q

Cited by 61 publications

References 40 publications

Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

Optical-lattice implementation scheme of a bosonic topological model with fermionic atoms

Infinite Dimensional Matrix Product States for Long-Range Quantum Spin Models

Contact Info

Product

Resources

About