Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems

Suzuki, Masuo

doi:10.1007/bf01609348

Cited by 788 publications

(481 citation statements)

References 11 publications

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“…8 It was later reformulated in order to be compatible with traditional DMRG implementations. 27,28 The TEBD is based on an iterative application of a Lie-Trotter-Suzuki decomposition 29,30 of the exact evolution operator for a small time step dt as…”

Section: Time-dependent Variational Principlementioning

confidence: 99%

Post-matrix product state methods: To tangent space and beyond

2013

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We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time evolution, excitations, and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well-defined quantum number. We present some illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post-matrix product methods.

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Section: Time-dependent Variational Principlementioning

confidence: 99%

Post-matrix product state methods: To tangent space and beyond

2013

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“…To this end, the one-dimensional quantum system is mapped onto a two-dimensional classical system by a Trotter-Suzuki decomposition [29][30][31]. Then, the additional dimension corresponds to the inverse temperature β.…”

Section: Numerical Resultsmentioning

confidence: 99%

Consequences of lattice imperfections and interchain couplings for the critical properties of spin-1/2 chain compounds

Sirker¹

2009

Condens. Matter Phys.

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To allow for a comparison of theoretical predictions for spin chains with experimental data, it is often important to take impurity effects as well as interchain couplings into account. Here we present the field theory for finite spin chains at finite temperature and calculate experimentally measurable quantities like susceptibilities and nuclear magnetic resonance spectra. For the interchain couplings we concentrate on geometries relevant for cuprate spin chains like Sr 2 CuO 3 and SrCuO 2 . The field theoretical results are compared to experimental as well as numerical data obtained by the density matrix renormalization group.

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“…Next, we need to apply the unitary expð−iHtÞ to this state. While many approaches to approximating this unitary on a quantum computer are known [47][48][49][50][51][52][53][54], here we use the simple approach of a Trotter-Suzuki decomposition [47,48]. We decompose the Hamiltonian H as a sum of noncommuting terms H ¼ P i H i , where the H i include both one-body and two-body terms, and make the approximation…”

Section: Quantum Simulation Of Time Evolutionmentioning

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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Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems

Cited by 788 publications

References 11 publications

Post-matrix product state methods: To tangent space and beyond

Post-matrix product state methods: To tangent space and beyond

Consequences of lattice imperfections and interchain couplings for the critical properties of spin-1/2 chain compounds

Hybrid Quantum-Classical Approach to Correlated Materials

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