This series consists of talks in the area of Condensed Matter.
We show that the numerical strong disorder renormalization group algorithm (SDRG) of Hikihara et.\ al.\ [{Phys. Rev. B} {\bf 60}, 12116 (1999)] for the one-dimensional disordered Heisenberg model naturally describes a tree tensor network (TTN) with an irregular structure defined by the strength of the couplings. Employing the holographic interpretation of the TTN in Hilbert space, we compute expectation values, correlation functions and the entanglement entropy using the geometrical properties of the TTN.
This has been a leading question in condensed matter physics since the discovery of the cuprate superconductors. In this talk I will review some of the DMRG and tensor network results for the ground states of these models. A key question I'll address is the issue of stripes: are the ground states striped? Do stripes compete with or induce d-wave superconductivity? Another question I'll address is: how well does 2D DMRG do in comparison with iPEPS and quantum Monte Carlo. I will also show recent results for a standard 3-band Hubbard model for the cuprates.
Roughly speaking, Many-Body Localization (MBL) refers to the state of a material that fails to thermalize. Though MBL has mostly been studied in quenched disordered systems, several authors have recently proposed that this phase could be realized in clean (translation invariant) systems too. In this talk, I will discuss this idea and ask to which extent an MBL phase can indeed be expected in systems without quenched disorder. Hopefully, the discussion shed also some light on the localization-delocalization transition for more generic many-body systems. From joint work with W.
We consider rather general spin-1/2 lattices with large coordination numbers Z.
Based on the monogamy of entanglement and other properties of the concurrence C,
we derive rigorous bounds for the entanglement between neighboring spins,
which show that C decreases for large Z. In addition, the concurrence C measures the deviation from mean-field behavior and can only vanish if the mean-field ansatz yields an exact ground state of the Hamiltonian. Motivated by these findings, we propose an improved mean-field ansatz by adding entanglement
We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector.
In the past few years substantial evidence has been collected that points to coexistence of charge correlations with long range superconductivity in underdoped cuprate superconductors. In this talk I will review some of this evidence, then show that a charge density wave with precisely the same signatures is a natural instability of an antiferromagnetic metal, and finally derive some phenomenological consequences, with special focus on quantum oscillation experiments.
Non-Abelian anyons are widely sought for the exotic fundamental physics they harbor as well as for their possible applications for quantum information processing. Currently, there are numerous blueprints for stabilizing the simplest type of non-Abelian anyon, a Majorana zero energy mode bound to a vortex or a domain wall. One such candidate system, a so-called "Majorana wire" can be made by judiciously interfacing readily available materials; the experimental evidence for the viability of this approach is presently emerging.