arXiv subjects

Stephan Rachel

Publications and source records attributed to Stephan Rachel.

103 records · Page 6Linked to original sources

arXiv2011

Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet

We compute the von Neumann and generalized Rényi entanglement entropies in the ground-state of the spin-1/2 antiferromagnetic Heisenberg model on the square lattice using the modified spin-wave theory for finite lattices. The addition of a staggered magnetic field to regularize the Goldstone modes associated with symmetry-breaking is shown to be essential for obtaining well-behaved values for the entanglement entropy. The von Neumann and Rényi entropies obey an area law with additive logarithmic corrections, and are in good quantitative agreement with numerical results from valence bond quantum Monte Carlo and density matrix renormalization group calculations. We also compute the spin fluctuations and observe a multiplicative logarithmic correction to the area law in excellent agreement with quantum Monte Carlo calculations.

cond-mat.str-el↗

arXiv2010

Critical theory of the topological quantum phase transition in a spin-2 chain

We systematically study the phase diagram of S=2 spin chain, by means of density-matrix renormalization group and exact diagonalization methods and confirm the presence of a dimer phase in the AKLT--SZH model. We find that the whole phase boundary between the dimer and SZH phases, including the multicritical point, is a critical line with the same central charge $c=5/2$. Finally, we propose and confirm that this line can be described by the $\rm SO(5)_1$ Wess-Zumino-Witten (WZW) conformal field theory.

cond-mat.str-el↗

arXiv2010

Entanglement from Charge Statistics: Exact Relations for Many-Body Systems

We present exact formulas for the entanglement and Rényi entropies generated at a quantum point contact (QPC) in terms of the statistics of charge fluctuations, which we illustrate with examples from both equilibrium and non-equilibrium transport. The formulas are also applicable to groundstate entanglement in systems described by non-interacting fermions in any dimension, which in one dimension includes the critical spin-1/2 XX and Ising models where conformal field theory predictions for the entanglement and Rényi entropies are reproduced from the full counting statistics. These results may play a crucial role in the experimental detection of many-body entanglement in mesoscopic structures and cold atoms in optical lattices.

cond-mat.mes-hall↗

arXiv2010

Charge solitons and their dynamical mass in 1-D arrays of Josephson junctions

We investigate the charge transport in one-dimensional arrays of Josephson junctions. In the interesting regime of "small charge solitons" (polarons), the charge dynamics is strongly influenced by the polaronic effects, i.e., by dressing of a Cooper pair by charge dipoles. In particular, the soliton's mass in this regime scales approximately as inverse square of the Josephson energy. We employ two theoretical techniques: the many body tight-binding approach and the mean-field approach. Results of the two approaches agree in the regime of "small charge solitons".

cond-mat.supr-con↗

arXiv2010

Topological Insulators and Mott Physics from the Hubbard Interaction

We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions. Applying a combination of Hartree-Fock theory, slave-rotor techniques, and topological arguments, we show that the topological band insulating phase persists up to quite strong interactions. Then we apply the slave-rotor mean-field theory and find a Mott transition at which the charge degrees of freedom become localized on the lattice sites. The spin degrees of freedom, however, are still described by the original Kane-Mele band structure. Gauge field effects in this region play an important role. When the honeycomb layer is isolated then the spin sector becomes already unstable toward an easy plane Neel order. In contrast, if the honeycomb lattice is surrounded by extra "screening" layers with gapless spinons, then the system will support a fractionalized topological insulator phase with gapless spinons at the edges. For large interactions, we derive an effective spin Hamiltonian.

cond-mat.str-el↗

arXiv2010

General Relation between Entanglement and Fluctuations in One Dimension

In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system. Using both analytical and numerical methods, we show that if particle number or spin is conserved, fluctuations in a subsystem obey identical scaling as a function of subsystem size, suggesting that fluctuations are a useful quantity for determining the scaling of entanglement, especially in higher dimensions. We investigate the effects of boundaries and subleading corrections for critical spin and bosonic chains.

cond-mat.stat-mech↗

arXiv2009

Theory of small charge solitons in one-dimensional arrays of Josephson junctions

We identify and investigate the new parameter regime of small charge solitons in one-dimensional arrays of Josephson junctions. We obtain the dispersion relation of the soliton and show that it unexpectedly flattens in the outer region of the Brillouin zone. We demonstrate Lorentz contraction of the soliton in the middle of the Brillouin zone as well as broadening of the soliton in the flat band regime.

cond-mat.supr-con↗

arXiv2009

Spontaneous Parity Violation in a Quantum Spin Chain

We report on a spontaneous breakdown of parity in the ground state of a spin Hamiltonian involving nearest-neighbor interactions. This occurs for a one-dimensional model where spins transform under the gauge field representation of QCD, the eight-dimensional adjoint representation of SU(3). The ground state spontaneously violates parity and is two-fold degenerate. In addition, the model possesses a non-vanishing topological string order parameter which we explicate analytically.

cond-mat.str-el↗

arXiv2009

Spin 3/2 dimer model

We present a parent Hamiltonian for weakly dimerized valence bond solid states for arbitrary half-integral S. While the model reduces for S=1/2 to the Majumdar-Ghosh Hamiltonian we discuss this model and its properties for S=3/2. Its degenerate ground state is the most popular toy model state for discussing dimerization in spin 3/2 chains. In particular, it describes the impurity induced dimer phase in Cr8Ni as proposed recently. We point out that the explicit construction of the Hamiltonian and its main features apply to arbitrary half-integral spin S.

cond-mat.str-el↗

arXiv2008

Exact models for trimerization and tetramerization in spin chains

We present exact models for an antiferromagnetic S=1 spin chain describing trimerization as well as for an antiferromagnetic S=3/2 spin chain describing tetramerization. These models can be seen as generalizations of the Majumdar-Ghosh model. For both models, we provide a local Hamiltonian and its exact three- or four-fold degenerate ground state wavefunctions, respectively. We numerically confirm the validity of both models using exact diagonalization and discuss the low lying excitations.

cond-mat.str-el↗

arXiv2008

Valence bond solid states with symplectic symmetry

We introduce a one-dimensional valence bond solid (VBS) state with symplectic symmetry SP(n) and construct the corresponding parent Hamiltonian. We argue that there is a gap in the spectrum. We calculate exactly the static correlation functions, which fall off exponentially. Hence the model introduced here shares all properties of the Haldane scenario for integer-spin quantum antiferromagnets. We further show that the VBS state possesses string order and discuss its generalization to higher dimensions.

cond-mat.str-el↗

arXiv2007

Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap

To begin with, we introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3bar of SU(3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and hence a Haldane gap in the excitation spectrum. We generalize some of our models to SU(n). Finally, we use the emerging rules for the construction of VBS states to argue that models of antiferromagnetic chains of SU(n) spins in general possess a Haldane gap if the spins transform under a representation corresponding to a Young tableau consisting of a number of boxes λwhich is divisible by n. If λand n have no common divisor, the spin chain will support deconfined spinons and not exhibit a Haldane gap. If λand n have a common divisor different from n, it will depend on the specifics of the model including the range of the interaction.

cond-mat.str-el↗

arXiv2007

Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians

We introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3bar of SU(3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and a Haldane gap in the excitation spectrum.

cond-mat.str-el↗