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1. Comb Tensor Networks

   Chepiga, Natalia; White, Steven R (June 2019, Physical review)

   In this paper we propose a special type of a tree tensor network that has the geometry of a comb—a one-dimensional (1D) backbone with finite 1D teeth projecting out from it. This tensor network is designed to provide an effective description of higher-dimensional objects with special limited interactions or, alternatively, one-dimensional systems composed of complicated zero-dimensional objects. We provide details on the best numerical procedures for the proposed network, including an algorithm for variational optimization of the wave function as a comb tensor network and the transformation of the comb into a matrix product state. We compare the complexity of using a comb versus alternative matrix product state representations using density matrix renormalization group algorithms. As an application, we study a spin-1 Heisenberg model system which has a comb geometry. In the case where the ends of the teeth are terminated by spin-1/2 spins, we find that Haldane edge states of the teeth along the backbone form a critical spin-1/2 chain, whose properties can be tuned by the coupling constant along the backbone. By adding next-nearest-neighbor interactions along the backbone, the comb can be brought into a gapped phase with a long-range dimerization along the backbone. The critical and dimerized phases are separated by a Kosterlitz-Thouless phase transition, the presence of which we confirm numerically. Finally, we show that when the teeth contain an odd number of spins and are not terminated by spin-1/2's, a special type of comb edge states emerge. 

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2. Bond-dependent slave-particle cluster theory based on density matrix expansion

   https://doi.org/10.1103/PhysRevB.107.115153  

   Jin, Zheting; Ismail-Beigi, Sohrab (March 2023, Physical Review B)

   Efficient and accurate computational methods for dealing with interacting electron problems on a lattice are of broad interest to the condensed matter community. For interacting Hubbard models, we introduce a cluster slave-particle approach that provides significant computational savings with high accuracy for total energies, site occupancies, and interaction energies. Compared to exact benchmarks using density matrix renormalization group for d-p Hubbard models, our approach delivers accurate results using two to three orders of magnitude lower computational cost. Our method is based on a slave-particle decomposition with an improved description of particle hoppings, and a density matrix expansion method where the interacting lattice slave-particle problem is turned into a set of overlapping real-space clusters which are solved self-consistently with appropriate physical matching constraints at shared lattice sites between clusters. 

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3. Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal

   https://doi.org/10.21468/SciPostPhysCore.7.3.044  

   Juhász, Róbert; Kovács, István A (July 2024, SciPost Physics Core)

   Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical renormalization group results for the paradigmatic model, the contact process, in the combined presence of these factors in both one and two-dimensional systems. Our results confirm our analytic arguments stating that the density vanishes smoothly at the extinction threshold, in a way characteristic of infinite-order transitions. This extremely smooth vanishing of the global density entails an enhanced exposure of the population to extinction events. At the same time, a reverse order parameter, the local persistence displays a discontinuity characteristic of mixed-order transitions, as it approaches a non-universal critical value algebraically with an exponent\beta_p'<1 ${\beta }_p\prime <1$. 

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4. Quantum Phase Transition in Strongly-Correlated Cavity Polaritons

   https://doi.org/10.1109/ACP.2018.8596265  

   Xue, Jian; Seo, Kangjun; Tian, Lin; Xiang, Tao (October 2018, IEEE Conference Proceeding for Asia Communications and Photonics Conference 2018)

   We study the quantum critical behavior in a multiconnected Jaynes-Cummings lattice using the density-matrix renormalization group method, where cavity polaritons exhibit a Mott-insulator-to-superfluid phase transition. We calculate the phase boundaries and the quantum critical points. 

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5. Realization of topological Mott insulator in a twisted bilayer graphene lattice model

   https://doi.org/10.1038/s41467-021-25438-1  

   Chen, Bin-Bin; Liao, Yuan Da; Chen, Ziyu; Vafek, Oskar; Kang, Jian; Li, Wei; Meng, Zi Yang (December 2021, Nature Communications)

   Abstract Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit. 

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