# Speeding up critical system dynamics through optimized evolution

## Abstract

The number of defects which are generated upon crossing a quantum phase transition can be minimized by choosing properly designed time-dependent pulses. In this work we determine what are the ultimate limits of this optimization. We discuss under which conditions the production of defects across the phase transition is vanishing small. Furthermore we show that the minimum time required to enter this regime is T{approx}{pi}/{Delta}, where {Delta} is the minimum spectral gap, unveiling an intimate connection between an optimized unitary dynamics and the intrinsic measure of the Hilbert space for pure states. Surprisingly, the dynamics is nonadiabatic; this result can be understood by assuming a simple two-level dynamics for the many-body system. Finally we classify the possible dynamical regimes in terms of the action s=T{Delta}.

- Authors:

- International School for Advanced Studies (SISSA), Via Beirut 2-4, I-34014 Trieste (Italy)
- (Germany)
- Institut fuer Quanteninformationsverarbeitung, Universitaet Ulm, D-89069 Ulm (Germany)
- NEST, Scuola Normale Superiore and Istituto di Nanoscienze-CNR, Piazza dei Cavalieri 7, I-56126 Pisa (Italy)
- (Italy)
- (ICTP), P.O. Box 586, I-34014 Trieste (Italy)

- Publication Date:

- OSTI Identifier:
- 22038618

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HAMILTONIANS; HILBERT SPACE; MANY-BODY PROBLEM; PHASE TRANSFORMATIONS; PURE STATES; TIME DEPENDENCE

### Citation Formats

```
Caneva, Tommaso, Institut fuer Quanteninformationsverarbeitung, Universitaet Ulm, D-89069 Ulm, Calarco, Tommaso, Montangero, Simone, Fazio, Rosario, Santoro, Giuseppe E., CNR-INFM Democritos National Simulation Center, Via Beirut 2-4, I-34014 Trieste, and International Centre for Theoretical Physics.
```*Speeding up critical system dynamics through optimized evolution*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.012312.

```
Caneva, Tommaso, Institut fuer Quanteninformationsverarbeitung, Universitaet Ulm, D-89069 Ulm, Calarco, Tommaso, Montangero, Simone, Fazio, Rosario, Santoro, Giuseppe E., CNR-INFM Democritos National Simulation Center, Via Beirut 2-4, I-34014 Trieste, & International Centre for Theoretical Physics.
```*Speeding up critical system dynamics through optimized evolution*. United States. doi:10.1103/PHYSREVA.84.012312.

```
Caneva, Tommaso, Institut fuer Quanteninformationsverarbeitung, Universitaet Ulm, D-89069 Ulm, Calarco, Tommaso, Montangero, Simone, Fazio, Rosario, Santoro, Giuseppe E., CNR-INFM Democritos National Simulation Center, Via Beirut 2-4, I-34014 Trieste, and International Centre for Theoretical Physics. Fri .
"Speeding up critical system dynamics through optimized evolution". United States. doi:10.1103/PHYSREVA.84.012312.
```

```
@article{osti_22038618,
```

title = {Speeding up critical system dynamics through optimized evolution},

author = {Caneva, Tommaso and Institut fuer Quanteninformationsverarbeitung, Universitaet Ulm, D-89069 Ulm and Calarco, Tommaso and Montangero, Simone and Fazio, Rosario and Santoro, Giuseppe E. and CNR-INFM Democritos National Simulation Center, Via Beirut 2-4, I-34014 Trieste and International Centre for Theoretical Physics},

abstractNote = {The number of defects which are generated upon crossing a quantum phase transition can be minimized by choosing properly designed time-dependent pulses. In this work we determine what are the ultimate limits of this optimization. We discuss under which conditions the production of defects across the phase transition is vanishing small. Furthermore we show that the minimum time required to enter this regime is T{approx}{pi}/{Delta}, where {Delta} is the minimum spectral gap, unveiling an intimate connection between an optimized unitary dynamics and the intrinsic measure of the Hilbert space for pure states. Surprisingly, the dynamics is nonadiabatic; this result can be understood by assuming a simple two-level dynamics for the many-body system. Finally we classify the possible dynamical regimes in terms of the action s=T{Delta}.},

doi = {10.1103/PHYSREVA.84.012312},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}