Imaginary-Time Matrix Product State Impurity Solver for Dynamical Mean-Field Theory

Wolf, F. Alexander; Go, Ara; McCulloch, Ian P.; Millis, Andrew J.; Schollwöck, Ulrich

doi:10.1103/physrevx.5.041032

Cited by 76 publications

(72 citation statements)

References 86 publications

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“…Compared to earlier calculations on the Bethe lattice [45], the computational cost of the impurity solver in this realistic setting increases by about an order of magnitude and numerical convergence into the ground state of the impurity model becomes much slower. This is the consequence of a strong increase of the ground-state entanglement, which then persists in the time-evolution.…”

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confidence: 89%

Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr2RuO4

Linden¹,

Zingl

Hubig

et al. 2020

Phys. Rev. B

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Using an imaginary-time matrix-product state (MPS) based quantum impurity solver we perform a realistic dynamical mean-field theory (DMFT) calculation combined with density functional theory (DFT) for Sr2RuO4. We take the full Hubbard-Kanamori interactions and spin-orbit coupling (SOC) into account. The MPS impurity solver works at essentially zero temperature in the presence of SOC, a regime of parameters currently inaccessible to continuous-time quantum Monte Carlo (CTQMC) methods, due to a severe sign problem. We show that earlier results obtained at high temperature, namely that the diagonal self-energies are nearly unaffected by SOC and that interactions lead to an effective enhancement of the SOC, hold even at low temperature. We observe that realism makes the numerical solution of the impurity model with MPS much more demanding in comparison to earlier works on Bethe lattice models, requiring several algorithmic improvements. arXiv:1909.02503v1 [cond-mat.str-el]

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confidence: 89%

Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr2RuO4

Linden¹,

Zingl

Hubig

et al. 2020

Phys. Rev. B

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“…Since there exist numerous available techniques enabling to solve efficiently this auxiliary problem, see, e.g., Refs. [40][41][42][43][44], this opens an exciting avenue for realistic modeling of many challenging materials, including predictions of ARPES spectra for complex orbitallyselective Mott insulators. Furthermore, since the Ghost-GA theory is based on the multi-orbital GA [14,17], it can be straightforwardly generalized to finite temperatures [45][46][47], to non-equilibrium problems [48,49], and to calculate linear response functions [50].…”

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confidence: 99%

Emergent Bloch excitations in Mott matter

et al. 2017

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We develop a unified theoretical picture for excitations in Mott systems, portraying both the heavy quasiparticle excitations and the Hubbard bands as features of an emergent Fermi liquid state formed in an extended Hilbert space, which is non-perturbatively connected to the physical system. This observation sheds light on the fact that even the incoherent excitations in strongly correlated matter often display a well defined Bloch character, with pronounced momentum dispersion. Furthermore, it indicates that the Mott point can be viewed as a topological transition, where the number of distinct dispersing bands displays a sudden change at the critical point. Our results, obtained from an appropriate variational principle, display also remarkable quantitative accuracy. This opens an exciting avenue for fast realistic modeling of strongly correlated materials.

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“…Recent developments [30][31][32] based on quantum chemical methods to define reduced basis sets for the exact diagonalization calculation permit inclusion of somewhat larger numbers of bath orbitals, but, at least as presently formulated, these methods work in a natural orbital basis that strongly mixes the bath and correlated orbitals, so that the sparsity structure mentioned above cannot be exploited. In a parallel development, ideas to solve the impurity problem using tensor networks [33] have recently started to show great promise [34][35][36].…”

Section: Hybrid Quantum-classical Approachmentioning

confidence: 99%

Hybrid Quantum-Classical Approach to Correlated Materials

et al. 2016

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Recent improvements in the control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around 100 logical qubits becomes available.

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Imaginary-Time Matrix Product State Impurity Solver for Dynamical Mean-Field Theory

Cited by 76 publications

References 86 publications

Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr2RuO4

Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr2RuO4

Emergent Bloch excitations in Mott matter

Hybrid Quantum-Classical Approach to Correlated Materials

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