1,149 research outputs found
Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets
We apply imaginary-time evolution, , to study relaxation
dynamics of gapless quantum antiferromagnets described by the spin-rotation
invariant Heisenberg Hamiltonian (). Using quantum Monte Carlo simulations,
we propagate an initial state with maximal order parameter (the
staggered magnetization) in the spin direction and monitor the expectation
value as a function of the time . Different
system sizes of lengths exhibit an initial size-independent relaxation of
toward its value the spontaneously symmetry-broken
state, followed by a size-dependent final decay to zero. We develop a generic
finite-size scaling theory which shows that the relaxation time diverges
asymptotically as where is the dynamic exponent of the low energy
excitations. We use the scaling theory to develop a way of extracting the
dynamic exponent from the numerical finite-size data. We apply the method to
spin- Heisenberg antiferromagnets on two different lattice geometries; the
two-dimensional (2D) square lattice as well as a site-diluted square lattice at
the percolation threshold. In the 2D case we obtain , which is
consistent with the known value , while for the site-dilutes lattice we
find . This is an improvement on previous estimates of . The scaling results also show a fundamental difference between the two
cases: In the 2D system the data can be collapsed onto a common scaling
function even when is relatively large, reflecting the
Anderson tower of quantum rotor states with a common dynamic exponent .
For the diluted lattice, the scaling works only for small , indicating a mixture of different relaxation time scaling
between the low energy states
Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
Theoretical studies of quantum phase transitions have suggested critical points with higher symmetries than those of the underlying Hamiltonian. Here we demonstrate a surprising emergent symmetry of the coexistence state at a strongly discontinuous phase transition between two ordered ground states. We present a quantum Monte Carlo study of a two-dimensional S=1/2 quantum magnet hosting the antiferromagnetic (AFM) and plaquette-singlet solid (PSS) states recently detected in SrCu2(BO3)2. We observe that the O(3) symmetric AFM order and the Z2 symmetric PSS order form an O(4) vector at the transition. The control parameter g (a coupling ratio) rotates the vector between the AFM and PSS sectors and there are no energy barriers between the two at the transition point gc. This phenomenon may be observable in SrCu2(BO3)2.First author draf
Glassy Phase of Optimal Quantum Control
We study the problem of preparing a quantum many-body system from an initial
to a target state by optimizing the fidelity over the family of bang-bang
protocols. We present compelling numerical evidence for a universal
spin-glass-like transition controlled by the protocol time duration. The glassy
critical point is marked by a proliferation of protocols with close-to-optimal
fidelity and with a true optimum that appears exponentially difficult to
locate. Using a machine learning (ML) inspired framework based on the manifold
learning algorithm t-SNE, we are able to visualize the geometry of the
high-dimensional control landscape in an effective low-dimensional
representation. Across the transition, the control landscape features an
exponential number of clusters separated by extensive barriers, which bears a
strong resemblance with replica symmetry breaking in spin glasses and random
satisfiability problems. We further show that the quantum control landscape
maps onto a disorder-free classical Ising model with frustrated nonlocal,
multibody interactions. Our work highlights an intricate but unexpected
connection between optimal quantum control and spin glass physics, and shows
how tools from ML can be used to visualize and understand glassy optimization
landscapes.Comment: Modified figures in appendix and main text (color schemes). Corrected
references. Added figures in SI and pseudo-cod
Anomalous quantum-critical scaling corrections in two-dimensional antiferromagnets
We study the N\'eel-paramagnetic quantum phase transition in two-dimensional
dimerized Heisenberg antiferromagnets using finite-size scaling of
quantum Monte Carlo data. We resolve the long standing issue of the role of
cubic interactions arising in the bond-operator representation when the dimer
pattern lacks a certain symmetry. We find non-monotonic (monotonic) size
dependence in the staggered (columnar) dimerized model, where cubic
interactions are (are not) present. We conclude that there is an irrelevant
field in the staggered model that is not present in the columnar case, but, at
variance with previous claims, it is not the leading irrelevant field. The new
exponent is and the prefactor of the correction
is large and comes with a different sign from that of the
formally leading conventional correction with exponent .
Our study highlights the possibility of competing scaling corrections at
quantum critical points.Comment: 6 pages, 6 figure
Broken symmetry in a two-qubit quantum control landscape
We analyze the physics of optimal protocols to prepare a target state with
high fidelity in a symmetrically coupled two-qubit system. By varying the
protocol duration, we find a discontinuous phase transition, which is
characterized by a spontaneous breaking of a symmetry in the
functional form of the optimal protocol, and occurs below the quantum speed
limit. We study in detail this phase and demonstrate that even though
high-fidelity protocols come degenerate with respect to their fidelity, they
lead to final states of different entanglement entropy shared between the
qubits. Consequently, while globally both optimal protocols are equally far
away from the target state, one is locally closer than the other. An
approximate variational mean-field theory which captures the physics of the
different phases is developed
Reinforcement Learning in Different Phases of Quantum Control
The ability to prepare a physical system in a desired quantum state is
central to many areas of physics such as nuclear magnetic resonance, cold
atoms, and quantum computing. Yet, preparing states quickly and with high
fidelity remains a formidable challenge. In this work we implement cutting-edge
Reinforcement Learning (RL) techniques and show that their performance is
comparable to optimal control methods in the task of finding short,
high-fidelity driving protocol from an initial to a target state in
non-integrable many-body quantum systems of interacting qubits. RL methods
learn about the underlying physical system solely through a single scalar
reward (the fidelity of the resulting state) calculated from numerical
simulations of the physical system. We further show that quantum state
manipulation, viewed as an optimization problem, exhibits a spin-glass-like
phase transition in the space of protocols as a function of the protocol
duration. Our RL-aided approach helps identify variational protocols with
nearly optimal fidelity, even in the glassy phase, where optimal state
manipulation is exponentially hard. This study highlights the potential
usefulness of RL for applications in out-of-equilibrium quantum physics.Comment: A legend for the videos referred to in the paper is available on
https://mgbukov.github.io/RL_movies
Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions
We study a generalized quantum spin ladder with staggered long range
interactions that decay as a power-law with exponent . Using large
scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG)
simulations, we show that this model undergoes a transition from a rung-dimer
phase characterized by a non-local string order parameter, to a symmetry broken
N\'eel phase. We find evidence that the transition is second order.In the
magnetically ordered phase, the spectrum exhibits gapless modes, while
excitations in the gapped phase are well described in terms of triplons --
bound states of spinons across the legs. We obtain the momentum resolved spin
dynamic structure factor numerically and find a well defined triplon band
evolves into a gapless magnon dispersion across the transition. We further
discuss the possibility of deconfined criticality in this model.Comment: 16 pages, 7 figure
Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
Theoretical studies of quantum phase transitions have suggested critical
points with higher symmetries than those of the underlying Hamiltonian. Here we
demonstrate a surprising emergent symmetry of the coexistence state at a
strongly discontinuous phase transition between two ordered ground states. We
present a quantum Monte Carlo study of a two-dimensional quantum magnet
hosting the antiferromagnetic (AFM) and plaquette-singlet solid (PSS) states
recently detected in SrCu(BO). We observe that the O(3) symmetric
AFM order and the Z symmetric PSS order form an O(4) vector at the
transition. The control parameter (a coupling ratio) rotates the vector
between the AFM and PSS sectors and there are no energy barriers between the
two at the transition point . This phenomenon may be observable in
SrCu(BO).Comment: 12 pages, 12 figure
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