scispace - formally typeset
Search or ask a question
Author

Markus Schmitt

Bio: Markus Schmitt is an academic researcher from University of California, Berkeley. The author has contributed to research in topics: Ising model & Quantum. The author has an hindex of 12, co-authored 26 publications receiving 426 citations. Previous affiliations of Markus Schmitt include Max Planck Society & University of Cologne.

Papers
More filters
Journal ArticleDOI
TL;DR: This work presents a versatile and efficient machine learning inspired approach based on a recently introduced artificial neural network encoding of quantum many-body wave functions that is comparable to or exceed the capabilities of state-of-the-art tensor network methods.
Abstract: The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose experimental exploration is currently pursued with strong efforts in quantum simulators. In this work we present a versatile and efficient machine learning inspired approach based on a recently introduced artificial neural network encoding of quantum many-body wave functions. We identify and resolve key challenges for the simulation of time evolution, which previously imposed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example, we study the dynamics of the paradigmatic two-dimensional transverse-field Ising model, as recently also realized experimentally in systems of Rydberg atoms. Calculating the nonequilibrium real-time evolution across a broad range of parameters, we, for instance, observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached timescales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.

107 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the ground state sector of the two-dimensional Kitaev honeycomb model regarding the occurrence of dynamical quantum phase transition (DQPT) and demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative.
Abstract: The notion of a dynamical quantum phase transition (DQPT) was recently introduced [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)] as the nonanalytic behavior of the Loschmidt echo at critical times in the thermodynamic limit. In this work the quench dynamics in the ground state sector of the two-dimensional Kitaev honeycomb model is studied regarding the occurrence of DQPTs. For general two-dimensional systems of BCS type it is demonstrated how the zeros of the Loschmidt echo coalesce to areas in the thermodynamic limit, implying that DQPTs occur as discontinuities in the second derivative. In the Kitaev honeycomb model DQPTs appear after quenches across a phase boundary or within the massless phase. In the 1d limit of the Kitaev honeycomb model it becomes clear that the discontinuity in the higher derivative is intimately related to the higher dimensionality of the nondegenerate model. Moreover, there is a strong connection between the stationary value of the rate function of the Loschmidt echo after long times and the occurrence of DQPTs in this model.

103 citations

Journal ArticleDOI
TL;DR: Nonergodic behavior in the quantum link model is demonstrated by obtaining a bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side of the transition.
Abstract: Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. This result is all the more surprising since the conventional many-body localization is conjectured to be unstable in two dimensions; hence the gauge invariance represents an alternative robust localization mechanism surviving in higher dimensions in the presence of interactions. Specifically, we demonstrate nonergodic behavior in the quantum link model by obtaining a bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side of the transition. We study the quantum dynamics in this system by introducing the method of ``variational classical networks,'' an efficient and perturbatively controlled representation of the wave function in terms of a network of classical spins akin to artificial neural networks. We identify a distinguishing dynamical signature by studying the propagation of line defects, yielding different light cone structures in the localized and ergodic phases, respectively. The methods we introduce in this work can be applied to any lattice gauge theory with finite-dimensional local Hilbert spaces irrespective of spatial dimensionality.

66 citations

Journal ArticleDOI
28 Feb 2018
TL;DR: In this paper, a perturbative network is constructed for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques.
Abstract: The efficient representation of quantum many-body states with classical resources is a key challenge in quantum many-body theory. In this work we analytically construct classical networks for the description of the quantum dynamics in transverse-field Ising models that can be solved efficiently using Monte Carlo techniques. Our perturbative construction encodes time-evolved quantum states of spin-1/2 systems in a network of classical spins with local couplings and can be directly generalized to other spin systems and higher spins. Using this construction we compute the transient dynamics in one, two, and three dimensions including local observables, entanglement production, and Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy of this approach by comparisons to exact results. We include a mapping to equivalent artificial neural networks, which were recently introduced to provide a universal structure for classical network wave functions.

52 citations

Journal ArticleDOI
TL;DR: Through the use of a SCID transfer system, it is demonstrated that under certain conditions, the production of Ig by Ly-1 B cells can be modulated by T cells, which suggests that the previous failure to observe T cell-dependent responses by Ly 1 B cells has been due to these B cells being "blind" to the antigens used and is not due to some inherent property ofThese B cells.
Abstract: Through the use of a SCID transfer system, we have demonstrated that under certain conditions, the production of Ig by Ly-1 B cells can be modulated by T cells. This modulation can take the form of enhanced isotype production or isotype-switch induction and to some extent appears to be dependent on the activation state of the T cells. Furthermore we have shown that Ly-1 B cells can mount an idiotypically restricted T cell-dependent immune response to the antigen PC-KLH. This result suggests that the previous failure to observe T cell-dependent responses by Ly-1 B cells has been due to these B cells being "blind" to the antigens used and is not due to some inherent property of these B cells. When one considers the previous reports of the substantial contribution of Ly-1 B cells to the natural serum immunoglobulin levels and the ability of T cells to affect Ig production by Ly-1 B cells documented in this report, it is clear that the interaction of T cells with the Ly-1 B-cell population is important in determining the "natural" serum Ig repertoire of the mouse.

47 citations


Cited by
More filters
Journal ArticleDOI

[...]

08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

Journal ArticleDOI
27 Jun 1996-Nature
TL;DR: A second selection process occurs during immune responses in which a new antibody repertoire is generated through somatic hypermutation, where only mutants binding antigen with high affinity survive to become memory cells.
Abstract: Each antibody-producing B cell makes antibodies of unique specificity, reflecting a series of ordered gene rearrangements which must be successfully performed if the cell is to survive. A second selection process occurs during immune responses in which a new antibody repertoire is generated through somatic hypermutation. Here only mutants binding antigen with high affinity survive to become memory cells. Cells expressing autoreactive receptors are counter-selected at both stages. This stringent positive and negative selection allows the generation and diversification of cells while rigorously controlling their specificity.

1,705 citations

Book
01 Jan 1957

1,574 citations