Related Experiment Video
Updated: Mar 26, 2026
09:04
Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
Published on: February 23, 2018
10.1K
Explicit Local Integrals of Motion for the Many-Body Localized State
Louk Rademaker1, Miguel Ortuño2
1Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
Physical Review Letters
|January 23, 2016
Summary
Researchers developed a new method to find local integrals of motion, essential for understanding the many-body localized phase. This technique precisely identifies these integrals, aiding the study of quantum systems and their transitions.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
Background:
- The many-body localized phase is a key concept in quantum physics.
- Characterizing this phase often involves identifying local integrals of motion.
Purpose of the Study:
- To introduce a novel Hilbert-space-preserving renormalization scheme.
- To exactly find local integrals of motion for characterizing the many-body localized phase.
Main Methods:
- The study employs a renormalization scheme based on the consecutive action of similarity transformations.
- Displacement operators are utilized within these transformations to iteratively find integrals of motion.
Main Results:
- The proposed method successfully identifies local integrals of motion.
- Demonstrated the localization and delocalization transition in interacting fermion chains with random potentials.
Conclusions:
- The developed renormalization scheme provides an exact method for finding local integrals of motion.
- This approach is applicable to studying many-body localization in various dimensions and disorder-free systems.
Related Concept Videos
01:21Principle of Linear Impulse and Momentum for a System of Particles
647
In the context of a system of particles moving relative to an inertial frame of reference, the equation of motion is a crucial tool for understanding the dynamics of the system. This equation, which accounts for external forces acting on each particle, plays a fundamental role in describing the system's behavior.
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...
647
01:13Kinetic Energy for a Rigid Body
596
Imagine a solid object involved in a general planar movement, with its center of mass pinpointed at a spot labeled G. The object's kinetic energy relative to an arbitrary point A can be quantified for each of its particles - the ith particle in this case. This measurement is achieved through the employment of the relative velocity definition. The position vector, known as rA, extends from point A to the mass element i.
596
01:14Equation of Motion: Center of Mass
790
The equation of motion for a single particle can be expanded to encompass a system of particles consisting of n particles. For any arbitrarily chosen particle within this system, the net force acting upon it is the aggregate of both internal and external forces. Extending this principle to all particles within the system results in the equation of motion for the entire assembly.
Internal forces between any pair of particles manifest as collinear pairs of equal magnitude but opposite directions,...
Internal forces between any pair of particles manifest as collinear pairs of equal magnitude but opposite directions,...
790
01:11Angular Momentum about an Arbitrary Axis
505
Imagine a rigid body with a mass denoted as 'm', which has its center of mass at point G and is rotating around an inertial reference frame. The angular momentum at an arbitrary point P can be calculated by taking the cross product of the position vector and linear momentum vector for each individual mass element.
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into...
The velocity of a mass element comprises its translational velocity and the relative velocity instigated by the body's rotation. Substituting the velocity equation into...
505
01:17Central-Force Motion
885
The central force system operates by exerting a force on an object directed towards a fixed point, typically the origin, with the force magnitude determined by the object's distance from this fixed point. In the context of an object with mass 'm,' polar coordinates are employed to express the equation of motion. Notably, the azimuthal component of force is nonexistent in this system. A comprehensive rewrite and integration of this equation reveal that the product of the squared...
885
01:22Equation of Motion: General Plane motion
684
In the context of a rigid body's movement within a general plane, it is important to understand that this motion is typically triggered by external forces or couple moments exerted onto it. This principle can be explained through Newton's second law, which stipulates the translational motion of the body's center of mass along each axis.
Moreover, the body's center of mass experiences a rotational effect as a result of these couple moments. This rotation can be articulated as the...
Moreover, the body's center of mass experiences a rotational effect as a result of these couple moments. This rotation can be articulated as the...
684