A route towards engineering many-body localization in real materials

The interplay of interactions and disorder in a quantum many body system may lead to the elusive phenomenon of many body localization (MBL). It has been observed under precisely controlled conditions in synthetic quantum many-body systems, but to detect it in actual quantum materials seems challenging. In this work, we present a path to synthesize real materials that show signatures of many body localization by mixing different species of materials in the laboratory. To provide evidence for the functioning of our approach, we perform a detailed tensor-network based numerical analysis to study the effects of various doping ratios of the constituting materials. Moreover, in order to provide guidance to experiments, we investigate different choices of actual candidate materials. To address the challenge of how to achieve stability under heating, we study the effect of the electron-phonon coupling, focusing on effectively one dimensional materials embedded in one, two and three dimensional lattices. We analyze how this coupling affects the MBL and provide an intuitive microscopic description of the interplay between the electronic degrees of freedom and the lattice vibrations. Our work provides a guideline for the necessary conditions on the properties of the ingredient materials and, as such, serves as a road map to experimentally synthesizing real quantum materials exhibiting signatures of MBL.Comment: 12 pages, 7 figure

Tensor network annealing algorithm for two-dimensional thermal states

Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark, we study the finite-temperature phase transition of the Ising model on an infinite square lattice, for which we obtain remarkable agreement with the exact solution. We then turn to study the finite-temperature Bose-Hubbard model in the limits of two (hard-core) and three bosonic modes per site. Our technique can be used to support the experimental study of actual effectively two-dimensional materials in the laboratory, as well as to benchmark optical lattice quantum simulators with ultracold atoms

Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials

Many-body localisation in disordered systems in one spatial dimension is typically understood in terms of the existence of an extensive number of (quasi)-local integrals of motion (LIOMs) which are thought to decay exponentially with distance and interact only weakly with one another. By contrast, little is known about the form of the integrals of motion in disorder-free systems which exhibit localisation. Here, we explicitly compute the LIOMs for disorder-free localised systems, focusing on the case of a linearly increasing potential. We show that while in the absence of interactions, the LIOMs decay faster than exponentially, the addition of interactions leads to the formation of a slow-decaying plateau at short distances. We study how the localisation properties of the LIOMs depend on the linear slope, finding that there is a significant finite-size dependence, and present evidence that adding a weak harmonic potential does not result in typical many-body localisation phenomenology. By contrast, the addition of disorder has a qualitatively different effect, dramatically modifying the properties of the LIOMS.Comment: 21 pages, 14 figures, replaced with final versio

A Compact Dual Band-Notched Circular Ring Printed Monopole Antenna for Super wideband Applications

In this article, a simple and compact dual band-notched (DBN) super wideband (SWB) printed monopole antenna (PMA) has been proposed. The proposed antenna composed of a circular PMA, which is connected through a 50-Ω triangular tapered microstrip fed line (TTMFL) and a round-cornered finite ground plane (RCFGP). It exhibits a very wide frequency band from 1.6–25 GHz (ratio band¬width of 15.63:1) with a voltage standing wave ratio (VSWR) ≤ 2. By employing a U-shaped parasitic element (USPE) near the RCFGP and a T-shaped protruded stub (TSPS) inside the radiating patch, a single band-notched (SBN) characteristic in the frequency band of 3.2–4.4 GHz (WiMAX/C-band) is generated. In order to realize the sec¬ond band-notched function for X-band satellite communication systems (7.2–8.4 GHz), a U-shaped slot (USS) has been inserted in the RCFGP. The overall dimension of the proposed antenna is 24x30x0.787 mm3 and occupies a relatively small space compared to the existing DBN an¬tennas. Good agreement has been attained between pre¬dicted and measured results

The classical two dimensional Heisenberg model revisited An SU 2 symmetric tensor network study

The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a continuous spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the O 3 non linear sigma model in 1 1 dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher dimensional ones like quantum chromodynamics in 3 1 dimensions , namely the phenomenon of asymptotic freedom. This should also exclude finite temperature transitions, but lattice effects might play a significant role in correcting the mainstream picture. In this work, we make use of state of the art tensor network approaches, representing the classical partition function in the thermodynamic limit over a large range of temperatures, to comprehensively explore the correlation structure for Gibbs states. By implementing an SU 2 symmetry in our two dimensional tensor network contraction scheme, we are able to handle very large effective bond dimensions of the environment up to amp; 967;effE amp; 8764;1500, a feature that is crucial in detecting phase transitions. With decreasing temperatures, we find a rapidly diverging correlation length, whose behaviour is apparently compatible with the two main contradictory hypotheses known in the literature, namely a finite T transition and asymptotic freedom, though with a slight preference for the secon

Pinwheel valence bond crystal ground state of the spin 1 2 Heisenberg antiferromagnet on the shuriken lattice

We investigate the nature of the ground state of the spin 1 2 Heisenberg antiferromagnet on the shuriken lattice by complementary state of the art numerical techniques, such as variational Monte Carlo VMC with versatile Gutzwiller projected Jastrow wave functions, unconstrained multivariable variational Monte Carlo mVMC , and pseudofermion pseudo Majorana functional renormalization group PFFRG PMFRG methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence bond crystal VBC orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest energy variational ground state, and it is obtained as an instability of the U 1 Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing order

Time evolution of many body localized systems in two spatial dimensions

Many-body localization is a striking mechanism that prevents interacting quantum systems from thermalizing. The absence of thermalization behaviour manifests itself, for example, in a remanence of local particle number configurations, a quantity that is robust over a parameter range. Local particle numbers are directly accessible in programmable quantum simulators, in systems of cold atoms even in two spatial dimensions. Yet, the classical simulation aimed at building trust in quantum simulations is highly challenging. In this work, we present a comprehensive tensor network simulation of a many-body localized systems in two spatial dimensions using a variant of an iPEPS algorithm. The required translational invariance can be restored by implementing the disorder into an auxiliary spin system, providing an exact disorder average under dynamics. We can quantitatively assess signatures of many-body localization for the infinite system: Our methods are powerful enough to provide crude dynamical estimates for the transition between localized and ergodic phases. Interestingly, in this setting of finitely many disorder values, which we also compare with simulations involving non-interacting fermions and for which we discuss the emergent physics, localization emerges in the interacting regime, for which we provide an intuitive argument, while Anderson localization is absent.Comment: 14 pages, 8 figures, replaced by final versio

Tensor network investigation of the double layer Kagome compound Ca10Cr7O28

Quantum spin liquids are exotic quantum phases of matter that do not order even at zero temperature. While there are several toy models and simple Hamiltonians that could host a quantum spin liquid as their ground state, it is very rare to find actual, realistic materials that exhibit their properties. At the same time, the classical simulation of such instances of strongly correlated systems is intricate and reliable methods are scarce. In this work, we investigate the quantum magnet Ca10Cr7O28 that has recently been discovered to exhibit properties of a quantum spin liquid in inelastic neutron scattering experiments. This compound has a distorted bilayer Kagome lattice crystal structure consisting of Cr5 ions with spin 1 2 moments. Coincidentally, the lattice structure renders a tensor network algorithm in 2D applicable that can be seen as a new variant of a projected entangled simplex state algorithm in the thermodynamic limit. In this first numerical investigation of this material that takes into account genuine quantum correlations, good agreement with the experimental findings is found. Our study contributes to uplifting tensor networks from conceptual tools to methods to describe real two dimensional quantum material