Numerical Quantum Simulation of Matteo Rizzi - KOMET 7 - JGU Mainz Vorstellung der Arbeitsgruppen WS 15-16
recent developments in control of quantum objects (e.g., cold atoms, trapped ions) General Framework quantum simulation of difficult problems for classical computers quantum engineering of synthetic states of matter
General Framework recent developments in control of quantum objects (e.g., cold atoms, trapped ions) quantum information look on many-body systems quantum simulation of difficult problems for classical computers relevant Hilbert corner & efficient numerics (e.g., tensor networks) quantum memories & processors quantum engineering of synthetic states of matter
General Framework recent developments in control of quantum objects (e.g., cold atoms, trapped ions) quantum information look on many-body systems quantum simulation of difficult problems for classical computers quantum engineering of synthetic states of matter relevant Hilbert corner & efficient numerics (e.g., tensor networks) quantum memories & processors MY FOCUS geometry + gauge fields + interactions topological states spin & orbital persistent currents anyons frustrated systems entanglement spectrum new, complementary approaches to cond-mat problems
Quantum Simulations & Engineering Computation on classical platforms Physicists Toy Models Quantum Many-Body Systems see also the AG Windpassinger / Schmidt-Kaler / Gerritsma
Quantum Simulations & Engineering Computation on classical platforms Quantum Many-Body Systems Physicists Toy Models Quantum Simulator & Engineering see also the AG Windpassinger / Schmidt-Kaler / Gerritsma
Quantum Simulations & Engineering Computation on classical platforms Quantum Many-Body Systems Physicists Toy Models Quantum Simulator & Engineering pose new questions? imagination into real-world see also the AG Windpassinger / Schmidt-Kaler / Gerritsma
Quantum Simulations & Engineering Computation on classical platforms Physicists Toy Models pose new questions? Quantum Many-Body Systems Quantum Simulator & Engineering imagination into real-world k d = k 1 k 2 = k d e x see also the AG Windpassinger / Schmidt-Kaler / Gerritsma
Interplay of geometry, gauges and interactions (1D) Wright et al., PRL 110, 025302 (2013) Iê - - Optimal regime for persistent current L a a W a 1.0 l=0.1 0.8 l=1.9 0.6 l=9.5 0.4 l=19.1 0.2 l=38.2 l=95.5 0.0 0.001 0.01 0.1 1 10 100 1000 g M.Cominotti, D. Rossini, M. Rizzi, F. Hekking, A. Minguzzi, PRL 113, 025301 (2014)
Q-Info driven numerics: DMRG & Tensor Networks Generic description of a many-body Hilbert space is exponentially expensive numbers
Q-Info driven numerics: DMRG & Tensor Networks Generic description of a many-body Hilbert space is exponentially expensive numbers Area-law for entanglement entropy generic state Physically accessible states Eisert, Cramer, Plenio RMP 82, 277 ( 10) Product states
generic state Q-Info driven numerics: DMRG & Tensor Networks Generic description of a many-body Hilbert space is exponentially expensive numbers Area-law for entanglement entropy Physically accessible states Eisert, Cramer, Plenio RMP 82, 277 ( 10) Product states
generic state Q-Info driven numerics: DMRG & Tensor Networks Generic description of a many-body Hilbert space is exponentially expensive Economic description by Tensor Networks : (variational RG schemes, DMRG) Schollwock, Ann. Phys. 326, 96 (2011) Area-law for entanglement entropy numbers numbers Physically accessible states Eisert, Cramer, Plenio RMP 82, 277 ( 10) Product states
Q-Info driven numerics: DMRG & Tensor Networks Generic description of a many-body Hilbert space is exponentially expensive Economic description by Tensor Networks : (variational RG schemes, DMRG) Schollwock, Ann. Phys. 326, 96 (2011) numbers numbers plenty of different decompositions in tensor products: MPS PEPS TTN see also the AG Orús MERA
Other recent works a. b. c. d. e. f. Tunable cold-atom platform for relativistic fermions & topological insulators PRA 82 043629 (2010) / PRL 105 190404 (2010) NJP 14 015007 (2012) / PoS 193, 036 (2014)
Other recent works a. b. c. d. e. f. Tunable cold-atom platform for relativistic fermions & topological insulators PRA 82 043629 (2010) / PRL 105 190404 (2010) NJP 14 015007 (2012) / PoS 193, 036 (2014) Trapped ultracold fermions in non-abelian gauge potentials Sci. Rep. 1, 43 (2011) + PRB 91, 115117 (2015)
Other recent works a. b. c. d. e. f. Tunable cold-atom platform for relativistic fermions & topological insulators PRA 82 043629 (2010) / PRL 105 190404 (2010) NJP 14 015007 (2012) / PoS 193, 036 (2014) Stability of quantum memories based on Kitaev-Majorana anyons PRB 88, 205142 (2013) + arxiv:1511.06592 + PRA 91, 042322 (2015) Trapped ultracold fermions in non-abelian gauge potentials Sci. Rep. 1, 43 (2011) + PRB 91, 115117 (2015) + (t) (t) tr / 2 t 0 (J 1 ) 1 0.98 0.96 0.94 0.92 0.9 (a) 0 50 100 150 200 time (J 1 ) 200 100 50 25 (c) (b) 0 50 100 150 200 time (J 1 ) 8 12 16 20 24 N N = 8 N = 12 N = 16 N = 20 N = 24
Other recent works a. b. c. d. e. f. Tunable cold-atom platform for relativistic fermions & topological insulators PRA 82 043629 (2010) / PRL 105 190404 (2010) NJP 14 015007 (2012) / PoS 193, 036 (2014) Stability of quantum memories based on Kitaev-Majorana anyons PRB 88, 205142 (2013) + arxiv:1511.06592 + PRA 91, 042322 (2015) Trapped ultracold fermions in non-abelian gauge potentials Sci. Rep. 1, 43 (2011) + PRB 91, 115117 (2015) Adaptive gauge approach to Tree Tensor Networks PRB, 90, 125154 (2014) arxiv:1510.01074 (NJP) + (t) (t) tr / 2 t 0 (J 1 ) 1 0.98 0.96 0.94 0.92 0.9 (a) 0 50 100 150 200 time (J 1 ) 200 100 50 25 (c) (b) 0 50 100 150 200 time (J 1 ) 8 12 16 20 24 N N = 8 N = 12 N = 16 N = 20 N = 24
Possible B.Sc. / M.Sc. Projects 1.contribute to the design of flat bands: * learn the basics of optical trapping of atoms & artificial creation of magnetic fields (gauge) * compute Bloch & Wannier of non-square lattices & use 2nd quantization to derive Hubbard model * help to decide the proper approximations
Possible B.Sc. / M.Sc. Projects 1.contribute to the design of flat bands: * learn the basics of optical trapping of atoms & artificial creation of magnetic fields (gauge) * compute Bloch & Wannier of non-square lattices & use 2nd quantization to derive Hubbard model * help to decide the proper approximations 2. investigate particles in a magnetic field: 2a) on a lattice: * learn about Peierls phase & Harper Hamiltonian * compute your own fractal Hofstadter butterfly 2a) in the continuum: * learn about Landau Levels and dimensional reduction * play with polynomials & co. OR with (existent) numerics * determine pseudopotentials for long-range interactions
Possible B.Sc. / M.Sc. Projects 3. get acquainted with anyons * learn about anyons and their funny exchange rules * solve exactly (via Gaussians) some fermionic problems (related to superconductors, spin-chains, topo. systems) * perform some own calculation on prototypical models (Fortran/Matlab/Mathematica) + learn about proposed physical implementations & speculate on new ones (via atoms, ions, etc.)
Possible B.Sc. / M.Sc. Projects 4. implement time-evol. in Tree-Tensor Networks: * learn about different solutions of the time-dep. Schrödinger Equation via Tensor Network Ansatz * apply them for periodic boundary conditions (new!) building on flexible existing libraries & codes * (master) exploit these tools to tackle non-equilibrium! [e.g., quenches in disordered systems]
Our group YOU! J. Jünemann M. Bischoff A. Haller Thanks for your attention!