Quantum Heat Statistics with Time-Evolving Matrix Product Operators

Popovic, Maria; Mitchison, Mark T.; Strathearn, Aidan; Lovett, Brendon W.; Goold, John; Eastham, P. R.

doi:10.1103/prxquantum.2.020338

Cited by 33 publications

(22 citation statements)

References 88 publications

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“…Interestingly, we find that the edge currents appear in the weak-coupling limit but are masked by the bulk currents at strong coupling. This finding contrasts with the usual expectation that exotic thermodynamic effects are more prone to arise in strong-coupling configurations [20][21][22][23][24][25][26][27][28][29][30][31]. Our exact analysis also helps to identify the range of parameters in which these dissipative edge currents can be experimentally realized.…”

contrasting

confidence: 65%

Robust nonequilibrium edge currents with and without band topology

Mitchison,

Rivas,

Martin-Delgado

2021

Preprint

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We study two-dimensional bosonic and fermionic lattice systems under nonequilibrium conditions corresponding to a sharp gradient of temperature imposed by two thermal baths. In particular, we consider a lattice model with broken time-reversal symmetry that exhibits both topologically trivial and nontrivial phases. Using a nonperturbative approach, we characterize the nonequilibrium current distribution in different parameter regimes. For both bosonic and fermionic systems weakly coupled to the reservoirs, we find chiral edge currents that are robust against defects on the boundary or in the bulk. This robustness not only originates from topological effects at zero temperature but, remarkably, also persists as a result of dissipative symmetries in regimes where band topology plays no role. Chirality of the edge currents implies that energy locally flows against the temperature gradient without any external work input. In the fermionic case, there is also a regime with topologically protected boundary currents, which nonetheless do not circulate around all system edges.

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contrasting

confidence: 65%

Robust nonequilibrium edge currents with and without band topology

Mitchison,

Rivas,

Martin-Delgado

2021

Preprint

Self Cite

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“…Since the TCL and the path integrals are equivalent [68], the irrelevant part of the density matrix in the former can potentially be determined using this technique, suggesting that the full density matrix can be determined. Alternative techniques to get insight into the bath could involve reaction coordinates, [69,70] auxiliary modes [71][72][73][74], counting statistics [75][76][77] and density matrix renormalization group [78][79][80][81].…”

Section: Discussionmentioning

confidence: 99%

Systematic Gorini, Kossakowski, Sudarshan and Lindblad Equation for Open Quantum Systems

Davidović¹

2021

Preprint

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In complex, open quantum systems, with many degrees of freedom, it is difficult to start a Markovian dynamics, let alone prepare a factorized system-environment state. Rather, the Markovian dynamics is an intertwining map of a completely positive (CP) non-Markovian dynamics. The Markovian master equation is usually not CP as such, and should be left alone if it works adequately well. Here we study how the intertwining Markovian dynamics can still be well approximated by a CP map. A coherent quantum dynamics can be systematically approximated by the CP, Geometric Arithmetic Master Equation (GAME), but this is not the case for an incoherent dynamics. This dichotomy is responsible for disagreeing claims if a CP Markovian master equation cannot have systematic accuracy. As an example, we show how the dynamical decoupling of a qubit breaks the perturbative, intertwining map, while fixing the accuracy of the GAME to near-exactness.

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“…This numerical approach allows one to simulate a system with linear coupling to a reservoir of harmonic oscillators, with arbitrary forms and strengths of system-reservoir coupling. The method has been applied to a variety of problems in open quantum systems [23][24][25][26][27][28][29][30][31]. It has also been used to to make conceptual connections to the process tensor (PT) formulation of open quantum systems [32,33].…”

Section: Imaginary-time Tempomentioning

confidence: 99%

Numerical evaluation and robustness of the quantum mean force Gibbs state

Chiu,

Strathearn,

Keeling

2021

Preprint

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We introduce a numerical method to determine the Hamiltonian of Mean Force (HMF) Gibbs state for a quantum system strongly coupled to a reservoir. The method adapts the Time Evolving Matrix Product Operator (TEMPO) algorithm to imaginary time propagation. By comparing the real-time and imaginary-time propagation for a generalized spin-boson model, we confirm that the HMF Gibbs state correctly predicts the steady state. We show that the numerical dynamics match the polaron master equation at strong coupling. We illustrate the potential of the imaginary-time TEMPO approach by exploring reservoir-induced entanglement between qubits.

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Quantum Heat Statistics with Time-Evolving Matrix Product Operators

Cited by 33 publications

References 88 publications

Robust nonequilibrium edge currents with and without band topology

Robust nonequilibrium edge currents with and without band topology

Systematic Gorini, Kossakowski, Sudarshan and Lindblad Equation for Open Quantum Systems

Numerical evaluation and robustness of the quantum mean force Gibbs state

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