Simulating many-body non-Hermitian 
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-symmetric spin dynamics

V., Varma, Anant; Das, Sourin

doi:10.1103/physrevb.104.035153

Cited by 9 publications

(3 citation statements)

References 36 publications

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“…One can use a Naimark dilation protocol [47] to dilate our non-Hermitian Hamiltonian to a higher dimensional Hermitian Hamiltonian that governs the system-ancilla state. The embedding of a non-Hermitian PT -symmetric Hamiltonian into a higher dimensional Hermitian one has already been studied previously [41,[48][49][50][51][52]. Applying this protocol in our model will give us an interaction Hamiltonian that accounts for unitary evolution of the system-ancilla state while the system subspace undergoes non-Hermitian dynamics exactly as shown in this paper.…”

Section: Discussionmentioning

confidence: 87%

A dynamical model for wavefunction collapse via non-Hermitian Hamiltonian

Gurpahul¹,

Singh²,

Banerjee³

2023

Preprint

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Ever since the formulation of quantum mechanics, there is very little understanding of the process of the collapse of a wavefunction. We have proposed a dynamical model to emulate the measurement postulates of quantum mechanics. We postulate that a non-Hermitian Hamiltonian operates during the process of measurement, which evolves any state to an attracting equilibrium state, thus, mimicking a "collapse". We demonstrate this using a 2-level system and then extend it to an N-level system. For a 2-level system, we also demonstrate that the dynamics generated by the Lindblad master equation can be replicated as an incoherent sum of the evolution by two separate non-Hermitian Hamiltonians. I. INTRODUCTIONAny standard quantum mechanics course or textbook [1]-[2] begins with a set of postulates. Three of them are termed the "measurement postulates", which we are currently interested in. These are: P1. A wavefunction, upon measurement of an observable, will always "collapse" to one of the eigenstates of the operator corresponding to that observable.P2. The probability of collapse to a particular eigenstate depends on the probability amplitudes associated with each eigenstate in the linear decomposition of the wavefunction.P3. Any repeated measurement immediately after a collapse gives the same eigenstate.

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Section: Discussionmentioning

confidence: 87%

A dynamical model for wavefunction collapse via non-Hermitian Hamiltonian

Gurpahul¹,

Singh²,

Banerjee³

2023

Preprint

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“…For this, we use the Naimark dilation protocol [37] to dilate a non-Hermitian Hamiltonian into a higher-dimensional Hermitian one. This protocol, also called the embedding formalism, has already been used previously to embed PT -symmetric non-Hermitian Hamiltonians into Hermitian Hamiltonians [23,[38][39][40][41][42]. Using this, we try to emulate the dynamics obtained in the first part of the von Neumann measurement scheme.…”

Section: Introductionmentioning

confidence: 99%

Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme

Singh,

Banerjee

2023

J. Phys. A: Math. Theor.

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The problem of how measurement in quantum mechanics takes place has existed since its formulation. Von Neumann proposed a scheme where he treated measurement as a two-part process— a unitary evolution in the full system-ancilla space and then a projection onto one of the pointer states of the ancilla (representing the ‘collapse’ of the wavefunction). The Lindblad master equation, which has been extensively used to explain dissipative quantum phenomena in the presence of an environment, can effectively describe the first part of the von Neumann measurement scheme when the jump operators in the master equation are Hermitian. We have proposed a non-Hermitian Hamiltonian formalism to emulate the first part of the von Neumann measurement scheme. We have used the embedding protocol to dilate a non-Hermitian Hamiltonian that governs the dynamics in the system subspace into a higher-dimensional Hermitian Hamiltonian that evolves the full space unitarily. We have obtained the various constraints and the required dimensionality of the ancilla Hilbert space in order to achieve the required embedding. Using this particular embedding and a specific projection operator, one obtains non-Hermitian dynamics in the system subspace that closely follow the Lindblad master equation. This work lends a new perspective to the measurement problem by employing non-Hermitian Hamiltonians.

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“…Alternatively, one can simulate the many-body Liouvillian dynamics on large-scale dissipative three-level superconducting qubit circuits via the control of driven frequencies and couplings between qubits [124], where the non-Hermitian ground state is prepared by quantum tomography [125] and entanglement can be measured in several protocols [126][127][128][129]. Other numeric or qubits quantum simulation methods for open systems are also applicable [130,131].…”

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confidence: 99%

Temporal evolution of one-dimensional fermion liquid with particle loss

Yi¹,

Lin²,

Lin³

et al. 2021

Preprint

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Intriguing phenomenon emerge with the sacrifice of Hermicity in quantum systems, which can be complemented in open system. Open quantum systems behave non-trivially from closed systems especially in temporal evolution. In this work, we study the dynamical properties of a generic one-dimensional fermionic system with particle loss. The short-time behavior of the system is described by a non-Hermitian effective Hamiltonian, while the long-time dynamics is governed by Lindblad master equation. We show that the time-dependent von Neumann entropy with spatial bipartition of the system has universal behaviors hinging on the Liouvillian spectra. On account of thermalization, the entropy increases rapidly in short time when turning on the quantum jumps. Whether the Liouvillian gap closes or not affects the long-time decaying. The left-right asymmetry of quasiparticles in momentum space is observed as a result of non-reciprocal hopping in the effective Hamiltonian induced by correlated quantum-jump operators. This will also induce an interaction-strength-independent momentum-space entanglement in early time. The phenomenon in momentum-space share the same origin with the renowned non-Hermitian skin effect.

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Simulating many-body non-Hermitian PT -symmetric spin dynamics

Cited by 9 publications

References 36 publications

A dynamical model for wavefunction collapse via non-Hermitian Hamiltonian

A dynamical model for wavefunction collapse via non-Hermitian Hamiltonian

Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme

Temporal evolution of one-dimensional fermion liquid with particle loss

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