Exploring Ground States of Quantum Spin Glasses by Quantum Monte Carlo Method

Chandra, Asit K.; Das, Arnab; Inoue, Jun‐ichi; Chakrabarti, Bikas K.

doi:10.1007/978-3-642-11470-0_11

Cited by 7 publications

(10 citation statements)

References 18 publications

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“…Evolving the state from t 0 to t, we get the state ρ(t), which has two terms as shown in equation (7). Now, we can numerically compute the inner product of the initial state |Ψ(0) with the eigenstates of the Hamiltonian to find the the state | Ψ(t) , and hence the detector function F n (t).…”

Section: Ising Dynamicsmentioning

confidence: 99%

See 1 more Smart Citation

Remotely detecting the signal of a local decohering process in spin chains

Sur¹,

Subrahmanyam²

2017

J. Phys. A: Math. Theor.

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Abstract. We study the dynamics of a one dimensional quantum spin chain evolving from unentangled or entangled initial state. At a given instant of time a quantum dynamical process (ex. measurement) is performed on a single spin at one end of the chain, decohering the system. Through the further unitary evolution, a signal propagates in the spin chain, which can be detected from a measurement on a different spin at later times. From the dynamical unitary evolution of the decohered state from the epoch time, it is possible to detect the occurrence of the dynamical process. The propagation of the signal for the dynamical process, and the speed of the signal are investigated for various spin models, viz. using the Ising, Heisenberg, and the transverse-XY dynamics.

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Section: Ising Dynamicsmentioning

confidence: 99%

“…These systems are generally studied from the quantum dynamics viewpoint, i.e. the evolution of an initial quantum many-body state through the time-dependent Schroedinger equation [7], and from a statistical mechanics viewpoint, i.e. the various thermodynamic phases and transitions [4,7].…”

Section: Introductionmentioning

confidence: 99%

Remotely detecting the signal of a local decohering process in spin chains

Sur¹,

Subrahmanyam²

2017

J. Phys. A: Math. Theor.

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“…Driving a system out of equilibrium is carried out in many ways. Most of the attention has been focused on quantum quenches [17], namely, sudden changes of the external parameters in the Hamiltonian controlling the unitary evolution of the closed system. One of the conventional methods of understanding the dynamics of a system after a quench is the Loschmidt echo (LE), which is a benchmark of the partial or full reappearance of the original state as a function of time [18,19].…”

Section: Introductionmentioning

confidence: 99%

Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field

Jafari

2016

J. Phys. A: Math. Theor.

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We study the ground state fidelity, fidelity susceptibility and quench dynamics of the extended quantum compass model in a transverse field. This model reveals a rich phase diagram which includes several critical surfaces depending on exchange couplings. We present a characterization of quantum phase transitions in terms of the ground state fidelity between two ground states obtained for two different values of external parameters. However, we derive scaling relations describing the singular behavior of fidelity susceptibility in the quantum critical surfaces. Moreover, we study the time evolution of the system after a critical quantum quench using the Loschmidt. We find that the revival times of Loschmidt echo are given by Trev = N/2vmax, where N is the size of the system and vmax is the maximum of lower bound group velocity of quasi-particles. Although the fidelity susceptibility shows the same exponent in all critical surfaces, the structure of the revivals after critical quantum quenches displays two different regimes reflecting different equilibration dynamics.

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“…One important and long-standing question concerns the existence of the fingerprints of a QPT on higher excited states (i.e., states with finite energy density with respect to the ground state). It is known that QPT has definitive signatures in the ground-state (and low-lying states close to it), as reflected in certain ground-state properties like the derivative of ground-state entanglement (concurrence) 5 , the ground-state fidelity susceptibility (see, e.g., 6 7 8 9 10 11 ) or scaling of ground-state entanglement entropy at the critical point(see, e.g., 12 13 14 ). For a physical (local) Hamiltonian, it is not unexpected for the states moderately close to the ground state (with vanishing energy density) to retain such direct mark of the singularity on them.…”

mentioning

confidence: 99%

Signature of a continuous quantum phase transition in non-equilibrium energy absorption: Footprints of criticality on higher excited states

Bhattacharyya

Dasgupta

Das

2015

Sci Rep

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Understanding phase transitions in quantum matters constitutes a significant part of present day condensed matter physics. Quantum phase transitions concern ground state properties of many-body systems, and hence their signatures are expected to be pronounced in low-energy states. Here we report signature of a quantum critical point manifested in strongly out-of-equilibrium states with finite energy density with respect to the ground state and extensive (subsystem) entanglement entropy, generated by an external pulse. These non-equilibrium states are evidently completely disordered (e.g., paramagnetic in case of a magnetic ordering transition). The pulse is applied by switching a coupling of the Hamiltonian from an initial value (λI) to a final value (λF) for sufficiently long time and back again. The signature appears as non-analyticities (kinks) in the energy absorbed by the system from the pulse as a function of λF at critical-points (i.e., at values of λF corresponding to static critical-points of the system). As one excites higher and higher eigenstates of the final Hamiltonian H(λF) by increasing the pulse height , the non-analyticity grows stronger monotonically with it. This implies adding contributions from higher eigenstates help magnifying the non-analyticity, indicating strong imprint of the critical-point on them. Our findings are grounded on exact analytical results derived for Ising and XY chains in transverse field.

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Exploring Ground States of Quantum Spin Glasses by Quantum Monte Carlo Method

Cited by 7 publications

References 18 publications

Remotely detecting the signal of a local decohering process in spin chains

Remotely detecting the signal of a local decohering process in spin chains

Quench dynamics and ground state fidelity of the one-dimensional extended quantum compass model in a transverse field

Signature of a continuous quantum phase transition in non-equilibrium energy absorption: Footprints of criticality on higher excited states

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