arXiv subjects

K. P. Schmidt

Publications and source records attributed to K. P. Schmidt.

At least 109 records · Page 6Linked to original sources

arXiv2010

Family of exactly solvable models with an ultimative quantum paramagnetic ground state

We present a family of two-dimensional frustrated quantum magnets solely based on pure nearest-neighbor Heisenberg interactions which can be solved quasi-exactly. All lattices are constructed in terms of frustrated quantum cages containing a chiral degree of freedom protected by frustration. The ground states of these models are dubbed ultimate quantum paramagnets and exhibit an extensive entropy at zero temperature. We discuss the unusual and extensively degenerate excitations in such phases. Implications for thermodynamic properties as well as for decoherence free quantum computation are discussed.

cond-mat.str-el↗

arXiv2010

Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study

We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.

cond-mat.str-el↗

arXiv2009

Neutron scattering evidence for isolated spin-1/2 ladders in (C$_5$D$_{12}$N)$_2$CuBr$_4$

Inelastic neutron scattering was used to determine the spin Hamiltonian for the singlet ground state system of fully deuterated BPCB, (C$_{5}$D$_{12}$N)$_{2}$CuBr$_{4}$. A 2-leg spin-1/2 ladder model, with $J_\bot = (1.09 \pm 0.01)$ meV and $J_\| = (0.296 \pm 0.005)$ meV, accurately describes the data. The experimental limit on the effective inter-ladder exchange constant is $|J_{\rm int}^{\rm eff}|\lesssim 0.006$ meV, and the limit on total diagonal, intra-ladder exchange is $|J_F+J_{F'}|\leq 0.1$ meV. Including the effects of copper to bromide covalent spin transfer on the magnetic form-factor, the experimental ratios of intra-ladder bond energies are consistent with the predictions of continuous unitary transformation.

cond-mat.str-el↗

arXiv2009

Perturbative approach to an exactly solved problem: the Kitaev honeycomb model

We analyze the gapped phase of the Kitaev honeycomb model perturbatively in the isolated-dimer limit. Our analysis is based on the continuous unitary transformations method which allows one to compute the spectrum as well as matrix elements of operators between eigenstates, at high order. The starting point of our study consists in an exact mapping of the original honeycomb spin system onto a square-lattice model involving an effective spin and a hardcore boson. We then derive the low-energy effective Hamiltonian up to order 10 which is found to describe an interacting-anyon system, contrary to the order 4 result which predicts a free theory. These results give the ground-state energy in any vortex sector and thus also the vortex gap, which is relevant for experiments. Furthermore, we show that the elementary excitations are emerging free fermions composed of a hardcore boson with an attached spin- and phase- operator string. We also focus on observables and compute, in particular, the spin-spin correlation functions. We show that they admit a multi-plaquette expansion that we derive up to order 6. Finally, we study the creation and manipulation of anyons with local operators, show that they also create fermions, and discuss the relevance of our findings for experiments in optical lattices.

cond-mat.other↗

arXiv2008

Supersolid phases of hardcore bosons on the square lattice: Correlated hopping, next-nearest neighbor hopping and frustration

We discuss the appearance of supersolid phases for interacting hardcore bosons on the square lattice when, in addition to the standard nearest neighbor hopping and repulsion, correlated or next-nearest neighbor hopping is present. Having in mind dimer-based quantum magnets in a field described by effective bosonic models of this kind, we put special emphasis on a comparison between the different cases of relative signs of the kinetic processes, which correspond to unfrustrated or frustrated magnetic models. In the unfrustrated case, we compare Quantum Monte Carlo simulations with a mean-field (classical) approach, which is shown to give qualitatively correct results. Using this classical approach for the frustrated case, we find that the phase diagram is generically richer than in the unfrustrated case. We also investigate in detail the differences between standard next-nearest neighbour and correlated hopping over the diagonal, with the conclusion that both cases are similar if checkerboard order is present at half-filling, while a supersolid phase can be stabilized without any adjacent solid phase only in the case of correlated hopping.

cond-mat.str-el↗

arXiv2008

Magnetization plateaux in an extended Shastry-Sutherland model

We study an extended two-dimensional Shastry-Sutherland model in a magnetic field where besides the usual Heisenberg exchanges of the Shastry-Sutherland model two additional SU(2) invariant couplings are included. Perturbative continous unitary transformations are used to determine the leading order effects of the additional couplings on the pure hopping and on the long-range interactions between the triplons which are the most relevant terms for small magnetization. We then compare the energy of various magnetization plateaux in the classical limit and we discuss the implications for the two-dimensional quantum magnet SrCu$_2$(BO$_3$)$_2$.

cond-mat.str-el↗

arXiv2008

Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking

We analyze the Kitaev model on the triangle-honeycomb lattice whose ground state has recently been shown to be a chiral spin liquid. We consider two perturbative expansions: the isolated-dimer limit containing Abelian anyons and the isolated-triangle limit. In the former case, we derive the low-energy effective theory and discuss the role played by multi-plaquette interactions. In this phase, we also compute the spin-spin correlation functions for any vortex configuration. In the isolated-triangle limit, we show that the effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at the isotropic point. We also compute the next-order correction which opens a gap and yields non-Abelian anyons.

cond-mat.other↗

arXiv2008

Mechanisms for Spin-Supersolidity in S=1/2 Spin-Dimer Antiferromagnets

Using perturbative expansions and the contractor renormalization (CORE) algorithm, we obtain effective hard-core bosonic Hamiltonians describing the low-energy physics of $S=1/2$ spin-dimer antiferromagnets known to display supersolid phases under an applied magnetic field. The resulting effective models are investigated by means of mean-field analysis and quantum Monte Carlo simulations. A "leapfrog mechanism", through means of which extra singlets delocalize in a checkerboard-solid environment via correlated hoppings, is unveiled that accounts for the supersolid behavior.

cond-mat.str-el↗

arXiv2008

Theory of magnetization plateaux in the Shastry-Sutherland model

Using perturbative continuous unitary transformations, we determine the long-range interactions between triplets in the Shastry-Sutherland model, and we show that an unexpected structure develops at low magnetization with plateaux progressively appearing at 2/9, 1/6, 1/9 and 2/15 upon increasing the inter-dimer coupling. A critical comparison with previous approaches is included. Implications for the compound SrCu$_2$(BO$_3$)$_2$ are also discussed: we reproduce the magnetization profile around localized triplets revealed by NMR, we predict the presence of a 1/6 plateau, and we suggest that residual interactions beyond the Shastry-Sutherland model are responsible for the other plateaux below 1/3.

cond-mat.str-el↗

arXiv2008

Creation and Manipulation of Anyons in the Kitaev Model

We analyze the effect of local spin operators in the Kitaev model on the honeycomb lattice. We show, in perturbation around the isolated-dimer limit, that they create Abelian anyons together with fermionic excitations which are likely to play a role in experiments. We derive the explicit form of the operators creating and moving Abelian anyons without creating fermions and show that it involves multi-spin operations. Finally, the important experimental constraints stemming from our results are discussed.

cond-mat.other↗

arXiv2008

Emergent Fermions and Anyons in the Kitaev Model

We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy excitations are emerging free fermions which are composed of hardcore bosons with an attached string of spin operators. The excitation spectrum is mapped onto that of a single particle hopping on a square lattice in a magnetic field. We also illustrate how to compute correlation functions in this framework. The present approach yields analytical perturbative results in the thermodynamical limit without using the Majorana or the Jordan-Wigner fermionization initially proposed to solve this problem.

cond-mat.other↗

arXiv2008

Comment on "Anyonic braiding in optical lattices"

We point out some major technical and conceptual mistakes which invalidate the conclusion drawn in "Anyonic braiding in optical lattices" by C. Zhang, V. W. Scarola, S. Tewari, and S. Das Sarma published in PNAS 104, 18415 (2007).

cond-mat.other↗

arXiv2007

Two-Dimensionality of Magnetic Excitations on the Trellis Lattice: (La,Sr,Ca)$_{14}$Cu$_{24}$O$_{41}$ and SrCu$_2$O$_3$

We explore the properties of magnetic excitations on the trellis lattice which is relevant for the so-called telephone-number compounds A$_{14}$Cu$_{24}$O$_{41}$ and the system SrCu$_2$O$_3$. The trellis lattice consists of two-leg ladders which are coupled in a strongly frustrated fashion. We use the effective model obtained for a single two-leg spin ladder to calculate the two-dimensional one-triplon dispersion and the corresponding one-triplon contribution to the dynamical structure factor. Special attention is laid on signatures of the frustrating inter-ladder magnetic exchange. A detailed suggestion is made for an experimental detection of this exchange in inelastic neutron scattering experiments.

cond-mat.str-el↗

arXiv2007

The fate of orbitons coupled to phonons

The key feature of an orbital wave or orbiton is a significant dispersion, which arises from exchange interactions between orbitals on distinct sites. We study the effect of a coupling between orbitons and phonons in one dimension using continuous unitary transformations (CUTs). Already for intermediate values of the coupling, the orbiton band width is strongly reduced and the spectral density is dominated by an orbiton-phonon continuum. However, we find sharp features within the continuum and an orbiton-phonon anti-bound state above. Both show a significant dispersion and should be observable experimentally.

cond-mat.str-el↗

arXiv2006

Single-particle versus pair condensation of hard-core bosons with correlated hopping

We investigate the consequences of correlated hopping on the ground state properties of hard-core bosons on a square lattice as revealed by extensive exact diagonalizations and quantum Monte Carlo simulations. While for non interacting hard-core bosons the effective attraction induced by the correlated hopping leads to phase separation at low density, we show that a modest nearest-neighbor repulsion suppresses phase separation, leading to a remarkable low-density pairing phase with no single particle Bose-Einstein condensation but long-range two-particle correlations, signaling a condensation of pairs. We also explain why the unusual properties of the pairing phase are a real challenge for standard one-worm quantum Monte Carlo simulations.

cond-mat.other↗

arXiv2006

One- and Two-Triplon Spectra of a Cuprate Ladder

We have performed inelastic neutron scattering on the near ideal spin-ladder compound La4Sr10Cu24O41, which will serve as a model system for the investigation of doped ladders. A key feature in the analysis was the separation of one-triplon and two-triplon scattering contributions due to an antiphase rung modulation. This enabled extraction of the one-triplon dispersion which has a spin gap of 26.4+/-0.3 meV, and for the first time two-triplon scattering is clearly observed. The exchange constants are determined by fitting the data to be Jleg=186 meV and Jrung=124 meV along the leg and the rung respectively. In addition to the surprisingly large difference between Jleg and Jrung a substantial ring exchange of Jcyc=31 meV was confirmed.

cond-mat.str-el↗

arXiv2006

Neutron scattering from a coordination polymer quantum paramagnet

Inelastic neutron scattering measurements are reported for a powder sample of the spin-1/2 quantum paramagnet $\rm Cu(Quinoxaline)Br_2$. Magnetic neutron scattering is identified above an energy gap of 1.9 meV. Analysis of the sharp spectral maximum at the onset indicates that the material is magnetically quasi-one-dimensional. Consideration of the wave vector dependence of the scattering and polymeric structure further identifies the material as a two-legged spin-1/2 ladder. Detailed comparison of the data to various models of magnetism in this material based on the single mode approximation and the continuous unitary transformation are presented. The latter theory provides an excellent account of the data with leg exchange $J_{\parallel}=2.0$ meV and rung exchange $J_{\perp}=3.3$ meV.

cond-mat.str-el↗

arXiv2005

Thermodynamics of Adiabatically Loaded Cold Bosons in the Mott Insulating Phase of One-Dimensional Optical Lattices

In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.

cond-mat.stat-mech↗