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Unit# Chaire de theorie de la matiere condensee

Chair

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Phase transition

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is use

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a for

Quantum Heisenberg model

The quantum Heisenberg model, developed by Werner Heisenberg, is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of

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Olivier Clément Romain Gauthé, Frédéric Mila

Using an SU(2) invariant finite-temperature tensor network algorithm, we provide strong numerical evidence in favor of an Ising transition in the collinear phase of the spin-1/2 J(1)-J(2) Heisenberg model on the square lattice. In units of J(2), the critical temperature reaches a maximal value of T-c/J(2 )similar or equal to 0.18 around J(2)/J(1) similar or equal to 1.0. It is strongly suppressed upon approaching the zero-temperature boundary of the collinear phase J(2)/J(1 )similar or equal to 0.6, and it vanishes as 1/log(J(2)/J(1)) in the large J(2)/J(1) limit, as predicted by Chandra et al., [Phys. Rev. Lett. 64, 88 (1990)]. Enforcing the SU(2) symmetry is crucial to avoid the artifact of finite-temperature SU(2) symmetry breaking of U(1) algorithms, opening new perspectives in the investigation of the thermal properties of quantum Heisenberg antiferromagnets.

Quantum many-body dynamics generically result in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of (high-temperature) thermal states. For accurate but approximate simulations one needs a way to keep track of essential (quantum) information while discarding inessential one. To this end, we first introduce the concept of the information lattice, which supplements the physical spatial lattice with an additional dimension and where a local Hamiltonian gives rise to well-defined locally conserved von Neumann information current. This provides a convenient and insightful way of capturing the flow, through time and space, of information during quantum time-evolution, and gives a distinct signature of when local degrees of freedom decouple from long-range entanglement. As an example, we describe such de-coupling of local degrees of freedom for the mixed-field transverse Ising model. Building on this, we secondly construct algorithms to time-evolve sets of local density matrices without any reference to a global state. With the notion of information currents, we motivate algorithms based on the intuition that information for statistical reasons flows from small to large scales. Using this guiding principle, we construct an algorithm that, at worst, shows two-digit convergence in time-evolutions up to very late times for diffusion process governed by the mixed-field transverse Ising Hamiltonian. While we focus on dynamics in 1D with nearest-neighbor Hamiltonians, the algorithms do not essentially rely on these assumptions and can in principle be generalized to higher dimensions and more complicated Hamiltonians.

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BaCuSi2O6 is a quasi-two-dimensional (2D) quantum antiferromagnet containing three different types of stacked, square-lattice bilayer hosting spin-1/2 dimers. Although this compound has been studied extensively over the last two decades, the critical applied magnetic field required to close the dimer spin gap and induce magnetic order, which exceeds 23 T, has to date precluded any kind of neutron scattering investigation. However, the HFM/EXED instrument at the Helmholtz-Zentrum Berlin made this possible at magnetic fields up to 25.9 T. Thus we have used HFM/EXED to investigate the field-induced ordered phase, in particular to look for quasi-2D physics arising from the layered structure and from the different bilayer types. From neutron diffraction data, we determined the global dependence of the magnetic order parameter on both magnetic field and temperature, finding a form consistent with 3D quantum critical scaling; from this we deduce that the quasi-2D interactions and nonuniform layering of BaCuSi2O6 are not anisotropic enough to induce hallmarks of 2D physics. From neutron spectroscopy data, we measured the dispersion of the strongly Zeeman-split magnetic excitations, finding good agreement with the zero-field interaction parameters of BaCuSi2O6. We conclude that HFM/EXED allowed a significant extension in the application of neutron scattering techniques to the field range above 20 T and in particular opened previously unavailable possibilities in the study of field-induced magnetic quantum phase transitions.