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Concept# Quantum spin liquid

Résumé

In condensed matter physics, a quantum spin liquid is a phase of matter that can be formed by interacting quantum spins in certain magnetic materials. Quantum spin liquids (QSL) are generally characterized by their long-range quantum entanglement, fractionalized excitations, and absence of ordinary magnetic order.
The quantum spin liquid state was first proposed by physicist Phil Anderson in 1973 as the ground state for a system of spins on a triangular lattice that interact antiferromagnetically with their nearest neighbors, i.e. neighboring spins seek to be aligned in opposite directions. Quantum spin liquids generated further interest when in 1987 Anderson proposed a theory that described high temperature superconductivity in terms of a disordered spin-liquid state.
Basic properties
The simplest kind of magnetic phase is a paramagnet, where each individual spin beha

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We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (i.e., self-conjugate 6 representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimerlike phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauthe, S. Capponi, and D. Poilblanc, Phys. Rev. B 99, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric projected entangled pair states (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations.

We generalize the construction of the spin-1/2 SU(2) resonating valence bond (RVB) state to the case of the self-conjugate 6 representation of SU(4). As for the case of SU(2) [J.-Y. Chen and D. Poilblanc, Phys. Rev. B 97, 161107(R) (2018)], we use the projected entangled pair state (PEPS) formalism to derive a simple (two-dimensional) family of generalized SU(4) RVB states on the square lattice. We show that, when longer-range SU(4)-singlet bonds are included, a local gauge symmetry is broken down from U(1) to Z(2), leading to the emergence of a short-range spin liquid. Evidence for the topological nature of this spin liquid is provided by the investigation of the Renyi entanglement entropy of infinitely long cylinders and of the modular matrices. Relevance to microscopic models and experiments of ultracold atoms is discussed.

2019Soudabeh Sheikholharam Mashhadi

From recent advances in solid state physics, a novel material classification scheme has evolved
which is based on the concept of topology and provides an understanding of different phenomena
ranging from quantum transport to unusual flavors of superconductivity. Spin-orbit
coupling is a major term in defining the topology of materials, and its interplay with electron electron
correlations yields novel, intriguing phenomena. In the weak to intermediate correlation
regime, spin-orbital entanglement leads to the emergence of topological insulators,
which constitute Dirac materials with 2D spin-polarized helical edge or surface
states and an insulating bulk. In the specific case of topological insulators,
theory predicts that their unique band structure leads to a high thermoelectric performance,
which is of practical relevance for energy conversion applications.In the strong correlation regime, the spin-orbit coupling removes the orbital degeneracy,
thereby enhancing quantum fluctuations of the spin-orbit entangled states. This in turn can
lead to the emergence of novel phases such as quantum spin liquids and unconventional
superconductivity. The Kitaev quantum spin liquid (QSL) is a topological state of matter that
exhibits fractionalized excitations in the form of Majorana fermions.
The main aim of this thesis was to study these novel states of matter in the form of two different
materials that fall in the weak and strong correlation regime, respectively. On this basis, it
should furthermore be explored whether benefit can be taken of their properties by combining
them with other quantum materials into heterostructures.In the first part of this thesis, nanoplatelets of bismuth chalcogenide-based 3D topological
insulators were grown by chemical vapor deposition, and characterized by magnetotransport
experiments. Having established charge transport characteristics of the single components, in
the aim to exploit their high thermoelectric efficiency, the lateral heteroctructures of them
are fabricated. Their investigation by scanning photocurrent microscopy revealed strong
photocurrent generation at the p-n junction. The obtained results demonstrate that such type of hybrid
heterostructure is a promising route to enhance the thermoelectric performance in nanostructured
devices.
In the second part of this thesis, the Kitaev spin liquid candidate, RuCl3 was studied. Raman spectroscopy on exfoliated
RuCl3 revealed a broad magnetic continuumat low energies which according to its particular
deviation from bosonic character is assigned to the fractionalized excitations. Furthermore,
in complementary charge transport experiments, it was found that themagnetic fluctuations
and structural changes in thismaterial are highly entangled, and influence the emergence of
the fractionalized excitations.
Finally, it was investigated whether the magnetic insulator character of ®-RuCl3 can be exploited
to alter the graphene band structure through a proximity effect in vertical graphene/
RuCl3 heterostructures. Measurements of their low-temperature, nonlocal resistance confirmed
the possibility to induce pure spin currents in this manner. At the same time, the
charge transport through the graphene served as a probe of the magnetic ordering in RuCl3,
although the complex magnetic behavior in this material necessitates more studies.