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Google's Tensor Processing Units (TPUs) are integrated circuits specifically built to accelerate and scale up machine learning workloads. They can perform fast distributed matrix multiplications and therefore be repurposed for other…
We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in…
There are three essential problems in computational relativistic chemistry: electrons moving at relativistic speeds, close lying states and dynamical correlation. Currently available quantum-chemical methods are capable of solving systems…
We have applied the momentum space version of the Density Matrix Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the new context. We have shown numerically that it is possible…
The practical success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad, Landau, Vazirani, and Vidick. The convergence…
The projection-based wave function (WF)-in-DFT embedding enables an efficient description of both the energetics and properties of large and complex chemical systems, with accuracy exceeding that of pure DFT. Recently, we have proposed…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…
We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
We have studied quantum data compression for finite quantum systems where the site density matrices are not independent, i.e., the density matrix cannot be given as direct product of site density matrices and the von Neumann entropy is not…
We generalize the recently introduced Density-Matrix Renormalization Group (DMRG-X) [Khemani et al, PRL 2016] algorithm to obtain Floquet eigenstates of one-dimensional, periodically driven many-body localized systems. This generalization…
The Density Matrix Renormalization Group (DMRG) is a state-of-the-art numerical technique for a one dimensional quantum many-body system; but calculating accurate results for a system with Periodic Boundary Condition (PBC) from the…
We present for the first time time-dependent density-matrix renormalization-group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy…
We derive an expansion of the functional renormalization (fRG) equations that treats the frequency and momentum dependencies of the vertices in a systematic manner. The scheme extends the channel-decomposed fRG equations to the frequency…
During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. The underlying matrix product state (MPS) ansatz is a low-rank decomposition of the full…
Quantum magnetism in low dimensions has been one of the central areas of theoretical research for many decades now. One of the key reasons for the long standing interest in this field has been the existence of simplified models, which serve…
We present a novel formulation of the vibrational density matrix renormalization group (vDMRG) algorithm tailored to strongly anharmonic molecules described by general high-dimensional model representations of potential energy surfaces. For…
In the nonrelativistic Schr\"{o}dinger equation, the total spin $S$ and spin projection $M$ are good quantum numbers. In contrast, spin symmetry is lost in the presence of spin-dependent interactions such as spin-orbit couplings in…
A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange $J_1$, $J_2$ between first and second neighbors. The modified algorithm yields accurate…
The density matrix renormalization group (DMRG) method is applied to the anisotropic Heisenberg chain at finite temperatures. The free energy of the system is obtained using the quantum transfer matrix which is iteratively enlarged in the…