arXiv subjects

Alexander Wietek

Publications and source records attributed to Alexander Wietek.

41 records · Page 3Linked to original sources

arXiv2018

Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems

We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of symmetry-adapted wave functions. Moreover, a parallelization scheme for the Hamiltonian-vector multiplication in the Lanczos procedure for distributed memory machines avoiding load balancing problems is proposed. We demonstrate that using these methods low-energy properties of systems of up to 50 spin-1/2 particles can be successfully determined.

cond-mat.str-el↗

arXiv2017

Studying Continuous Symmetry Breaking using Energy Level Spectroscopy

Tower of States analysis is a powerful tool for investigating phase transitions in condensed matter systems. Spontaneous symmetry breaking implies a specific structure of the energy eigenvalues and their corresponding quantum numbers on finite systems. In these lecture notes we explain the group representation theory used to derive the spectral structure for several scenarios of symmetry breaking. We give numerous examples to compute quantum numbers of the degenerate groundstates, including translational symmetry breaking or spin rotational symmetry breaking in Heisenberg antiferromagnets. These results are then compared to actual numerical data from Exact Diagonalization.

cond-mat.str-el↗

arXiv2016

Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice

We investigate the $J_1$-$J_2$ Heisenberg model on the triangular lattice with an additional scalar chirality term and show that a chiral spin liquid is stabilized in a sizeable region of the phase diagram. This topological phase is situated in between a coplanar $120^\circ$ Néel ordered and a non-coplanar tetrahedrally ordered phase. Furthermore we discuss the nature of the spin-disordered intermediate phase in the $J_1$-$J_2$ model. We compare the groundstates from Exact Diagonalization with a Dirac spin liquid wavefunction and propose a scenario where this wavefunction describes the quantum critical point between the $120^\circ$ magnetically ordered phase and a putative $\mathbb{Z}_2$ spin liquid.

cond-mat.str-el↗

arXiv2016

Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields

We show that, in the presence of a $π/2$ artificial gauge field per plaquette, Mott insulating phases of ultra-cold fermions with $SU(N)$ symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by a multiplet of $N$ low-lying singlet excitations for periodic boundary conditions, and by chiral edge states described by the $SU(N)_1$ Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for $N$ between $3$ and $9$, and by a parton construction based on a set of $N$ Gutzwiller projected fermionic wave-functions with flux $π/N$ per triangular plaquette. Experimental implications are briefly discussed.

cond-mat.quant-gas↗

arXiv2015

Nature of chiral spin liquids on the kagome lattice

We investigate the stability and the nature of the chiral spin liquids which were recently uncovered in extended Heisenberg models on the kagome lattice. Using a Gutzwiller projected wave function approach -- i.e. a parton construction -- we obtain large overlaps with ground states of these extended Heisenberg models. We further suggest that the appearance of the chiral spin liquid in the time-reversal invariant case is linked to a classical transition line between two magnetically ordered phases.

cond-mat.str-el↗