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Quantum Phase Transitions of Frustrated Heisenberg Antiferromagnets: a Comprehensive Renormalization Approach

Stefan Scheidl

Published Jan 1, 2008• 0 citations
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Abstract

Institut fu¨r Theoretische Physik, Universit¨at zu K¨oln, Zu¨lpicher Str. 77, D-50937 K¨oln, Germany(Dated: February 2, 2008)We develop a novel renormalization approach for frustrated quantum antiferromagnets. It isdesigned to consistently treat spin-wave interactions all over the magnetic Brillouin zone, includinghigh-energy modes in outer regions as well as low energy modes in the center. Focusing on theparadigmatic J

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Institut fu¨r Theoretische Physik, Universit¨at zu K¨oln, Zu¨lpicher Str. 77, D-50937 K¨oln, Germany(Dated: February 2, 2008)We develop a novel renormalization approach for frustrated quantum antiferromagnets. It isdesigned to consistently treat spin-wave interactions all over the magnetic Brillouin zone, includinghigh-energy modes in outer regions as well as low energy modes in the center. Focusing on theparadigmatic J
We develop a novel renormalization approach for frustrated quantum antiferromagnets. It is designed to consistently treat spin-wave interactions all over the magnetic Brillouin zone, including high-energy modes in outer regions as well as low energy modes in the center. Focusing on the paradigmatic J1J_1J1​-J2J_2J2​ model, we find a unifying description of the second-order transition between the Néel phase and the paramagnetic phase and the first-order transition between the Néel phase and the columnar phase. Our approach provides explicit results for the renormalized values of the spin stiffness and spin-wave velocity characterizing the low-energy magnons in the Néel phase.
Institut fu¨r Theoretische Physik, Universita¨t zu K¨oln, De-50937 K¨oln, Germany(Dated: December 16, 2013)Landau-Zener transitions in a Lipkin-Meshkov-Glick model are considered, both as a single systemand in a lattice where each individual site hosts a realization of the corresponding many-bodyproblem. The single site mean-field problem is conceptually different from many other non-linearLandau-Zener models - it does not support any hysteresis and a new phenomenon appears whereadiabaticity totaly breaks down. More precisely, thisbreakdown occurs for isolated classical solutionspropagating on a separatrix in phase space and during the Landau-Zener sweep they get locked toa fixed point which prohibits adiabatic following. Quantum fluctuations tend to destabilize thesesolutions such that for moderate particle numbers the phenomenon is lost. At the quantum levelit is also shown that the non-adiabatic corrections P of the single site problem obey a power-lawdependenceon the Landau-Zenersweep velocity λ in the adiabatic regime, i.e. P ∼ λ
A spin-[Formula: see text] lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the [Formula: see text] point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.
Valentin Murg Max-Planck-Institut fu¨r Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany Ignacio Cirac Max-Planck-Institut fu¨r Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany Frank Verstraete Fakulta¨t fu¨r Physik, Universita¨t Wien, Boltzmanngasse 5, A-1090 Wien, Austria The formulation of renormalization group methods in terms of matrix product states (MPS) has the big advantage that it allows one to describe time evolution. This opens up the possibility of simulating the non-equilibrium properties of spin chains, a topic that is currently very relevant given the recent breakthroughs in creating strongly-correlated quantum spin systems, for example in optical lattices [1].