Finite-temperature dynamical correlations using the microcanonical ensemble and the Lanczos algorithm

Long, M W; Prelovšek, P.; Shawish, S. El; Karadamoglou, J.; Zotos, X.

doi:10.1103/physrevb.68.235106

Cited by 91 publications

(100 citation statements)

References 15 publications

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“…(12) can be contrasted with the predicted scaling of the Hilbert space variant of a whole system which should be proportional to (D + 1) −1 for the expectation value of a local operator [31]. The results of the current research are also relevant for methodologies for measuring finitetemperature dynamical correlations [32] without performing the complete TDSE evolution of the whole system.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness

et al. 2013

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We consider the decoherence of a quantum system S coupled to a quantum environment E. For states chosen uniformly at random from the unit hypersphere in the Hilbert space of the closed system S + E we derive a scaling relationship for the sum of the off-diagonal elements of the reduced density matrix of S as a function of the size D E of the Hilbert space of E. This sum decreases as 1/ √ D E as long as D E 1. We test this scaling prediction by performing large-scale simulations which solve the time-dependent Schrödinger equation for a ring of spin-1/2 particles, four of them belonging to S and the others to E, and for this ring with small world bonds added in E and/or between S and E. The spin-1/2 particles experience nearest-neighbor interactions that are identical for the interactions within S and random for the interactions within E and between S and E, or that are all identical. Provided that the time evolution drives the whole system from the initial state toward a scaling state, a state which has similar properties as states belonging to the class of quantum states for which we derived the scaling relationship, the scaling prediction holds. We examine various interaction parameters and initial states for our model system to find whether or not the time evolution reaches the class of states that have the scaling property. For the homogeneous ring we find that the evolution for select initial states does not reach these scaling states. This conclusion is not modified if we add some homogeneous random connections. For a ring we find that some randomness in the interaction parameters is required so that most initial configurations are driven toward the scaling state. Furthermore, if the amount of randomness is small the time required to reach the scaling states may be very large. For the case of all random interactions in E the ring is driven toward the scaling state. Adding small world bonds between S and E with random interaction strengths may decrease the time required to reach the scaling state or may prevent the scaling state from being reached. For the latter case we show that increasing the complexity of the environment by adding extra connections within the environment suffices to observe the predicted scaling behavior.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness

et al. 2013

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“…For details we refer to Ref. [17]; e.g., the largest available size for the t-V model is thus L = 28. Besides the σ(ω) spectra it is instructive to also show the normalized integrated intensity I(ω).…”

Section: Methodsmentioning

confidence: 99%

“…Particularly appropriate at large enough T is the microcanonical Lanczos method (MCLM) 17 . The MCLM uses the idea that dynamical autocorrelations (in a large enough system) can be evaluated with respect to a single wavefunction |Ψ provided that the energy deviation…”

Section: Methodsmentioning

confidence: 99%

Anomalous scaling of conductivity in integrable fermion systems

et al. 2004

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We analyze the high-temperature conductivity in one-dimensional integrable models of interacting fermions: the t-V model (anisotropic Heisenberg spin chain) and the Hubbard model, at half-filling in the regime corresponding to insulating ground state. A microcanonical Lanczos method study for finite size systems reveals anomalously large finite-size effects at low frequencies while a frequency-moment analysis indicates a finite d.c. conductivity. This phenomenon also appears in a prototype integrable quantum system of impenetrable particles, representing a strong-coupling limit of both models. In the thermodynamic limit, the two results could converge to a finite d.c. conductivity rather than an ideal conductor or insulator scenario.

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“…That is, the (full) MBL requires that both, C 0 and S 0 , are finite. For the calculation of imbalance correlations we employ the microcanonical Lanczos method (MCLM) [42,43] on finite systems of maximum length L = 14 forn = 1 (forn = 1/2 see the Supplement [41] ). The high frequency resolution is achieved by large number of Lanczos steps N L = 10…”

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confidence: 99%

Absence of full many-body localization in the disordered Hubbard chain

2016

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We present numerical results within the one-dimensional disordered Hubbard model for several characteristic indicators of the many-body localization (MBL). Considering traditionally studied charge disorder (i.e., the same disorder strength for both spin orientations) we find that even at strong disorder all signatures consistently show that while charge degree of freedom is non-ergodic, the spin is delocalized and ergodic. This indicates the absence of the full MBL in the model that has been simulated in recent cold-atom experiments. Full localization can be restored if spin-dependent disorder is used instead. 71.27.+a, 71.30.+h, 71.10.Fd Introduction.-The many-body localization (MBL) is a phenomenon whereby an interacting many-body system localizes due to disorder, proposed [1, 2] in analogy to the Anderson localization of noninteracting particles [3, 4]. The MBL physics has attracted a broad attention of theoreticians. Yet, it has so far been predominantly studied within the prototype model, i.e., the one-dimensional (1D) model of interacting spinless fermions with random potentials, equivalent to the anisotropic spin-1/2 Heisenberg chain with random local fields. Emerging from these studies are main hallmarks of the MBL state of the system: a) the Poisson many-body level statistics [5][6][7][8][9], in contrast to the Wigner-Dyson one for normal ergodic systems, b) vanishing of d.c. transport at finite temperatures T > 0, including the T → ∞ limit [10][11][12][13][14][15][16][17], c) logarithmic growth of the entanglement entropy [18][19][20], as opposed to linear growth in generic systems, d) an existence of a set of local integrals of motion [21][22][23][24], and e) a non-ergodic time evolution of (all) correlation functions and of quenched initial states [25][26][27][28][29]. Because of these unique properties, the MBL can be used, e.g. to protect quantum information [30,31]. For more detailed review see Refs. [32,33].The experimental evidence for the MBL comes from recent experiments on cold atoms in optical lattices [34][35][36][37] and ion traps [38]. In particular, for strong disorders, experiments reveal non-ergodic decay of the initial density profile in uncoupled [34] and coupled [36] 1D fermionic chains, as well as the vanishing of d.c. mobility in a 3D disordered lattice [35]. In contrast to most numerical studies, being based on the spinless fermion models, the cold-atom experiments simulate a disordered Hubbard model. The latter has been much less investigated theoretically [34,39,40], whereby results show that density imbalance might be non-ergodic at strong disorder [34,39], in accordance with experiments [34,36].The essential difference with respect to the interacting spinless model is that Hubbard model has two local degrees of freedom: charge (density) and spin. The aim of this Letter is to present numerical evidence that in the case of a (charge) potential disorder and finite repulsion U > 0 (as e.g. realized in the cold-atom experiments), both degrees behave qualitatively different. In...

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Finite-temperature dynamical correlations using the microcanonical ensemble and the Lanczos algorithm

Cited by 91 publications

References 15 publications

Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness

Quantum decoherence scaling with bath size: Importance of dynamics, connectivity, and randomness

Anomalous scaling of conductivity in integrable fermion systems

Absence of full many-body localization in the disordered Hubbard chain

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